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ASSIST User Manual

1. LAM C 1E 5 Failure rate of computers SPACE CAF ARRAY 1 3 OF BOOLEAN Failed computers in Triad A CBF ARRAY 1 3 OF BOOLEAN Failed computers in Triad B PSF ARRAY 1 3 OF BOOLEAN Failed power supplies START 9 OF FALSE DEATHIF COUNT CAF gt 1 2 3 computers in Triad A failed DEATHIF COUNT CBF gt 1 2 3 computers in Triad B failed FOR I IN T5243 IF NOT CAF I RANTO CAF I TRUE BY LAM C Computer failure in Triad A IF NOT CBF I RANTO CBF I TRUE BY LAM C Computer failure in Triad B IF NOT PSF I RANTO CAF I TRUE CBF I TRUE PSF I TRUE BY LAM P Power supply failure ENDFOR This method of modeling the system leads to a semi Markov model with 70 states and 138 transitions to model this relatively simple system As can be seen from this example modeling systems with semi Markov models is still an art even when using the ASSIST program As with any language once the user becomes proficient in using the ASSIST language he can see more easily how to generate more elegant models Often a model can be made considerably smaller by using fewer state space variables to describe the system states although this practice sometimes leads to rather complex TRANTO and DEATHIF statements By using state space variables to represent the number of failed computers in each t
2. 12 1 8 2 Trigonometric functions The trigonometric functions are listed in table 6 Examples of expressions using these trigonometric functions are PI 4 0 ARCTAN 1 0 TWOPI 2 0 PI COSPI COS PI SINHALFPI SIN PI 2 0 ANG ARCSIN 0 5 VAL SORT COS LAMBDA PI 2 SIN MU TWOPI 2 Table 6 Built in Trigonometric Functions Function Parameter type SIN Real Real sin x COS Real Real cos x TAN Real Real tan x ARCSIN Real Real sin x ARCCOS Real Real cos x ARCTAN Real Real tan x 12 1 8 3 Combinatorial functions The combinatorial functions are listed in table 7 Examples of expressions using these combinatorial functions are FOO COMB 12 5 FACT 4 FOOBAR PERM 12 2 FOO_BAR GAM 6 113 Table 7 Built in Combinatorial Functions Function Parameter type Result Description FACT Int Int n COMB Int int Int ua 4 k n k PERM Int int Int paler j n k GAM Real Real T x Table 8 Built in Array List Functions Parameter type Description Scalar dim x SUM a x b a Y x b i l Scalar Where a b are scalar air 1 ifr true Bool array Y r r sS 0 if r false dim r count p r q p Y r 8 q i l Bool list Int Where p q are scalar List Scalar y ye list and y Sy Vy list List Scalar y ye list and y2y Vy list Bool list Bool scalar COUNT ilist gt 0 Bool list B
3. MONITORED SENSOR FAILURE MODEL LAMBDA S 10E 6 Failure rate of sensors LAMBDA M 1E 6 Failure rate of monitors MU 1 3E 4 Mean recovery time for first fault SIG 1 1E 4 S D of recovery time for first fault MU 2 1E 4 Mean recovery time for second fault SIG 2 2E 5 S D of recovery time for second fault COV 2 98 Coverage for second failure SPACE NS 0 3 Number of active sensors NFS 0 3 Number of failed active sensors NM 0 3 Number of working monitors START 2 0 3 y DEATHIF 2 NFS NS Majority of sensors failed DEATHIF 2 NFS NS AND NM lt NS Half of the sensors fail and the number of monitors working is less than the number of active sensors IF NS gt O TRANTO NFS BY NS NFS LAMBDA S Sensor failure IF NM 1 TRANTO NM BY LAMBDA M Monitor failure IF NS gt 2 NFS AND NFS 0 THEN First fault recovery IF NM gt O TRANTO NS NFS NM BY MU 1 SIG 1 NM NS Loss of monitored sensor IF NM NS TRANTO NS NFS BY MU 1 SIG 1 NS NM NS Loss of unmonitored sensor ENDIF IF NS 2 NFS AND NFS 0 THEN Second fault recovery RANTO NS NFS BY MU 2 SIG 2 COV 2 Successfully removed failed sensor RANTO NS BY MU 2 SIG 2 1 0 COV 2 Mistakenly removed nonfaulty sensor ENDIF The semi Markov model that is generated for this example contains 20 states
4. e xref This option is the same as the map option e loadmap This option is used to request a load map of the internal data structures and memory allocation generated during parsing of the input file The load map information is extremely tech nical The option remains in the language for verification purposes and because it is useful in some rare instances Its use is not recommended Use of xref is recommended instead The default is not having a load map e ss This option forces ASSIST to print the warning level as part of each warning message For example instead of WARNING the message will read WARNING SEVERITY 3 The default is not displaying the warning severity 93 we3 This option forces ASSIST to display three letter abbreviations in warning and error messages such as ERR and WRN The default is not abbreviating the words ERROR and WARNING bat This option causes ASSIST to execute in batch mode In batch mode the command line is echoed to standard error usually the user s monitor screen The default is not to echo the com mand line used to invoke ASSIST wid nnn This option specifies the maximum line length plus one The default is 80 charac ters and results in an effective input line length of 79 characters tab nnn This option specifies how many spaces are equivalent to a tab character The default is four spaces per tab nest nnn Spe
5. 43 ELSE TRANTO NFP IX BY 3 NFP IX LAM C Failures of computers when other triad has no failures yet ENDIF ENDFOR IF SUM NFP 0 THEN TRANTO NFP 1 NFP 2 NFS SAME TRUE BY 3 LAM PS Power supply failures when no previous computer failures have occurred ELSE IF SAME THEN TRANTO 2 2 2 FALSE BY 2 NFS LAM PS Failure of a power supply not connected to another previously failed computer NOTE State 2 2 2 F i is an aggregation of several death states IF SUM NFP NFS lt 3 TRANTO 1 1 1 TRUE BY LAM_PS Failed power supply connected to a previously failed computer ELSE TRANTO 2 2 2 FALSE BY 3 NFS LAM PS Failure of a power supply not connected to another previously failed computer NOTE State 2 2 2 F 5 is an aggregation of several death states KI ENDIF ENDIF The second ASSIST input file leads to a semi Markov model with only 25 states and 29 transitions as compared to the first strategy which required 70 states and 138 transitions to model the same system However this input file is much more difficult to understand and verify Automatic lumping of death states further reduces the model to 7 states with 29 transitions 16 6 Triad With Intermittent Faults The next example shows a triad subject to intermittent faults This triad ha
6. If placed around a statement containing an erroneous FUNCTION or IMPLICIT reference these commands will detail how the macro was expanded and may shed more light on why the context was erroneous For example DEBUGS EXPANDS IF F I THEN DEBUGS NONES ENDIF 91 D 3 Cross Reference Map The xref command line option can be used to produce a cross reference map of all identifier block IF and FOR references throughout the input file For example assist foo xref or C_OPTION XREF D 4 Load Map The loadmap command line option can be used to produce an extremely technical dump of the data structures and memory layout after the input file has been parsed and before rule generation begins The load map is written to the log file and might be of limited use to a select few technically oriented users but if you ask for it then you get it 92 Appendix E Command Line Options The ASSIST command line allows the user to specify options These options control a number of parameters and allow the user more control over how the ASSIST program executes Options must be preceded by a slash under VMS as in map and they must be preceded by a dash under UNIX as in map Options may be specified in upper or lowercase The normal UNIX case sensitivity does not apply to the ASSIST command line options Options may also be typed into the input file via C OPTION commands These commands mu
7. and the IDENTIFIER TABLE OVERFLOW SPECIFY I N OPTIONS currently N 200 I 400 This error indicates that the user is using more numbers or identifiers than the current symbol table can hold The user must increase the table size with either the n2num or i anynum command line option or in a C OPTION I num or C_OPTION N num statement as the first line of the input file The default is i 400 for workstations and i 200 for the IBM PC The default is n2200 for workstations and n 50 for the IBM PC IDENTIFIER TABLE OVERFLOW SPECIFY I N OPTIONS currently N 200 1 400 gt This error is the VMS equivalent of the previous error INTEGER VALUE EXPECTED gt This error indicates that the resulting type of an expression was not an integer The token at the end of the expression in error is echoed ILLEGAL CHARACTER char gt This error indicates that a special character not allowed by the ASSIST syntax was encountered Certain characters including the exclamation mark the percent sign and all non printing characters are illegal in ASSIST INFIX EXPRESSION LIST OVERFLOW SPECIFY O OPTION id gt This error indicates that a very long expression was being parsed The expression was longer than ever anticipated If the expression cannot be simplified then increase
8. For Markov analysis programs requiring a dif ferent form of input for the Markov model a simple program could be written to modify the model description file Describing a system in the ASSIST abstract input language forces the reliability engineer to under stand clearly the fault tolerance strategies of the system and the abstract description is also useful for communicating and validating the system model This paper describes the ASSIST computer program and input language and shows a few simple examples For a detailed tutorial on how to use the SURE and ASSIST programs the reader is referred to reference 5 The basic concepts of the ASSIST program are introduced in section 2 The syntax of the ASSIST input language is detailed in section 3 and techniques for reducing the size of the generated model are described in section 4 Section 5 presents the algorithm used to generate the semi Markov reliability model from the input description The files generated by the program are described in section 6 Section 7 leads the reader through a number of example problems Finally the commands for executing the ASSIST program are presented in section 8 followed by the Concluding Remarks 11 Basic Concepts The ASSIST program is based on concepts that are used to design compilers The ASSIST input language defines rules for generating a model The model states are defined by a set of state space vari ables which represent system state characteri
9. MU 3 PSI MU XI TAU PSI MU XI TAU PSI MU lt XI TAU PSI MU lt XI TAU PSI lt MU XI gt TAU PSI lt MU XI gt TAU TAU gt MU amp MU gt RHO TAU lt RHO TAU gt MU amp MU gt RHO TAU lt RHO The in this context is applied to Boolean values The result will be TRUE whenever both sides are TRUE or both sides are FALSE 54 In some instances in order to avoid overflow underflow it is assumed that the user really intended to do real arithmetic These instances are integer lt negative integer gt real integer lt large positive integer gt real lt integer gt lt integer gt real For example 2 3 0 125 10 9 1 000 000 000 10 11 gt 100 000 000 000 0 3 2 gt 1 5 9 DIV 2 gt 4 integer result 9 MOD 2 1 integer result 55 Appendix B BNF Language Description Appendix B gives a complete description of the ASSIST language syntax using the Backus Naur Form BNF grammar lt program gt lt setup section gt lt start section gt lt rule section gt setup stat seq start stat seqg rule stat seq any setup sec stat any start sec stat any rule sec stat lt pre rule global stat gt lt global stat gt lt any statement gt reserved word lt setup section gt start section lt rule section
10. NUMBER OF STATES IN MODEL 2 NUMBER OF TRANSITIONS IN MODEL 1 1 DEATH STATES AGGREGATED INTO STATE 1 Note that the first line of each page begins with the name of the ASSIST input file a3 ast fol lowed by the date and time of the run 3 16 94 10 20 49 a m and ends with the program and version number which processed the input file ASSIST 7 1 NASA LaRC followed by the page number 33 The input file is listed next Note that the line numbers are not typed into the input file They are automatically generated for reference purposes The four corresponding lines in the input file a3 ast are SPACE A B C D START 2 OF 3 1 OF 2 1 IF C 2 TRANTO C C41 BY A B C D DEATHIF C gt 2 The last five lines in the log file give statistics on the parsing time rule generation time number of model states number of model transitions and number of aggregated death states respectively Note that the number of aggregated death states is a count of how many transitions resulted in death not a count of the number of unique state n tuples which are death states Error messages appear in the log file directly below the line that is in error The wedge charac ter points to the approximate location within the line where the error occurred For example 0006 ABC AAA 2 ERROR IDENTIFIER NOT DEFINED AAA 0007 15 1 3 Object File The objec
11. START NI triad Count of working in triad 0 Count of active failed in triad 0 Count of benign failed in triad 46 KKK KKK KKK KKK KKK KKK ck ckckck ck ck KK ck ck ck kk KKK KKK KKK KKK KK KKK KKK KKK kck ck ck ck kk KK K KK COMPONENT triad kk kk kk ck CkCckckckckckckckckckckokckckck ck ckckck ck ck ck ck ck ck ck kk KKK KKK KKK KEK KKK KKK KKK KKK ck kck ck ck ck kk ASSI LH RT TWA triad TFA triad lt NI triagd IF NW triad gt 0 RANTO NW triad NFA triad H BY NW_triad L_I_triad Intermittent fault arrival IF NFB_triad gt 0 TRANTO NFB_triad NFA_triad BY FAST ALP_triad Benign fault goes active IF NFA_triad gt 0 THE Active Intermittent faults TRANTO NFA_triad NFB_triad BY FAST BET_triad Active fault goes benign IF NW_triad NFB_triad 2 THEN degrade to simplex IF NW_triad 2 HEN RANTO NFA triad NW triad 1 BY FAST R_D_triad ELSE IF NW triad 0 THEN RANTO NFA triad NFB triad 1 BY FAST R D triad ELSE RANTO NFA triad NW triad 0 BY FAST 0 5 R D triad RANTO NFA triad NFB triad 0 BY FAS 0 5 R D triag ENDIF ENDIF ELSE degrade by one TRANTO NFA_triad BY FAST R_D_triad KKK KKK KKK KEK KKK KKK KKK KKK KKK c
12. erated error messages will give enough detail to make an appropriate correction For extremely rare instances in which more information is helpful there are certain tricks that one can use to get that infor mation These are described herein D 1 C OPTION Statement The command line option statement can be used at the beginning of an input file to specify special command line options that must always be used to correctly process the file in question For example if foo ast were to begin with C OPTION W NONE The wznone option may be omitted from the command line as illustrated assist foo The values specified in the C OPTION statement override any values explicitly given on the com mand line For example if C OPTION W NONE is specified as the first line of the ASSIST input file foo ast and if the command line is specified as assist foo w all no warnings will be printed because the C OPTION W NONE statement overrides the option as spec ified on the command line D 2 Debug Statement Ba The DEBUG statement can be used to print out internal information to the log file Internals can be very technical so not very much will be said about this statement The source code provides an analysis for advanced users who understand the internals of ASSIST There are two forms of the debug statement that may be of use to an intermediate user These are DEBUGS EXPANDS DEBUGS NONES
13. 1 6 0 0 2 5 1 0 LAMBDA defines a transition from SURE state 1 which was ASSIST state 6 0 0 to SURE state 2 which was ASSIST state 5 1 0 at an exponential rate with mean A The comment feature can be turned off by adding the line COMMENT 0 to the ASSIST input file Following the state transitions are three comment lines containing the following statistics describing the model the number of model states the number of model transitions and the number of distinct TOTAL is a prototype user interface program that generates ASSIST input files from a more abstract description of the system ref 8 32 death states encountered in building the model These statistics are printed within comment delimiters and the SURE program will ignore them Unless errors or warnings are encountered these three com ment lines will be the last three lines in the model file For example NUMBER OF STATES IN MODEL 2 NUMBER OF TRANSITIONS IN MODEL 6 6 DEATH STATES AGGREGATED INTO STATE 1 If errors or warnings are detected the number of errors and warnings are printed as comments at the end of the model file For example 0048 ERRORS 0001 WARNING 15 1 2 Log File The log listing file contains a listing of the ASSIST input file plus various information to aid the user in checking the correctness of the generated model The listing file has the alog file exten
14. 6 3 1 2 1 10 3 1 2 2 2 LAMBDA_S 7 3 0 2 2 10 3 1 2 2 3 0 LAMBDA P 8 3 1 1 0 11 3 0 0 0 FAST 1 0 1 1 DELTA 8 3 1 1 0 1 3 2 1 0 DEATH 3 1 LAMBDA P 8 3 1 1 0 12 3 1 1 1 1 LAMBDA_S 9 3 0 1 1 12 3 1 1 1 3 0 LAMBDA P 10 3 1 2 2 12 3 1 1 1 FAST 2 2 1 DELTA 10 3 1 2 2 1 3 2 2 2 DEATH 3 1 LAMBDA_P 11 3 0 0 0 13 3 1 0 0 3 0 LAMBDA P 12 3 1 1 1 13 3 1 0 0 FAST 1 1 1 DELTA 12 3 1 1 1 1 3 2 1 1 DEATH 3 1 LAMBDA P 13 3 1 0 0 1 3 2 0 0 DEATH 3 1 LAMBDA P NUMBER OF STATES IN MODI 13 NUMBER OF TRANSITIONS IN MODEL 24 6 DEATH STATES AGGREGATED INTO STATE 1 E ES 16 2 Many Triads With Pool of Spares The example above can be expanded to model a system with several triads and a pool of spares using array state space variables If two or more processors in an active triad fail the system fails As long as spares are available a faulty processor in a triad is replaced from the spare pool If no spares are available the triad is broken up and the nonfaulty processors are added to the spare pool This example is very similar to the first example except that the DEATH F statement and TRANTO statements pertaining to triads must be put inside FOR constructs so that all
15. This error indicates that a non numeric quantity occurred in a numeric expression It usually appears when Booleans are found when numeric expressions are expected BOOLEAN ITEM EXPECTED token gt This error indicates that something other than a Boolean item was encountered when the syntax for ASSIST required a Boolean item The token fund instead of the Boolean item is echoed BOOLEAN ITEM EXPECTED token BUILT IN FUNCTION func gt This error indicates that something other than a Boolean item was encountered in the parameter list for a built in function such as COUNT when the syntax for ASSIST required a Boolean item The token found instead of the Boolean item is echoed BOOLEAN OPERATOR IN AN ARITHMETIC EXPRESSION op gt This error indicates that something other than a Boolean operator was encountered in an arithmetic expression when the syntax for ASSIST required a Boolean item The token found instead of the Boolean item is echoed A relational operator was probably found in a numeric expression The operator that is illegal in the expression is echoed BOOLEAN VALUE EXPECTED token This error indicates that the resulting type of an expression was not a Boolean The token at the end of the expression in error is echoed BUILT IN FUNCTION SIZE REQUIRES AN ARRAY token gt This error indicates that something other than an array was encountered as
16. but not to a value less than 38 COMMAND LINE OPTION TOO TINY wid nnn limit 38 gt This error is the VMS version of the previous error message COMMAND LINE OPTION VALUE TOO BIG MAX ALLOWED 32767 gt This error indicates that the value entered for a command line option was bigger than could be parsed The user should use a smaller value T J CONSTANT IDENTIFIER NAME NOT UNIQUE TO FIRST 12 CHARS SURE WILL NOT BI ABLE TO SOLVE THIS MODEL id gt This error indicates that two different named constants have different names in ASSIST but will have the same name in SURE due to truncation to 12 characters by SURE This message occurs only for named numeric constants since Boolean constants are not written to the model output file The error is usually caused when a constant array is declared For each item in a constant array a constant scalar name is generated by appending the subscript s used to index the array to the end of the array name For example in the case of the doubly subscripted array named LAMBDA REC identifiers such as LAMBDA_REC_4_11 will be generated These identifi ers are not unique to the first 12 characters To solve this problem use a shorter array name DISK QUOTA EXCEEDED PLEASE CONTACT SYSTEM MANAGER foo ext gt This error indicates that there is not enough disk space left to open or write to the specified file When a u
17. that the longest file name that can be used for an ASSIST input file name ast file is one less than the longest file name allowed by the operating system on systems that allow four character extents such as UNIX and VMS FILE NOT FOUND joo ast gt This error indicates that the specified input file does not exist The user probably misspelled the file name FUNCTION BODY STORAGE OVERFLOW SPECIFY B OPTION id This error indicates that there were very many or very large FUNCTION and IMPLICIT func tions There was not enough body token storage allocated To fix the problem try to use more FUNCTIONs and IMPLICITs and eliminate common subexpressions If that does not help then 70 increase the body storage on the command line or in a C_OPTION B num statement as the first line of the input file The default is b 1024 for workstations and b 256 for the IBM PC FUNCTION BODY STORAGE OVERFLOW SPECIFY B OPTION id gt This error is the VMS equivalent of the previous error FUNCTION IMPLICIT NESTING LEVEL OVERFLOW SPECIFY NEST OPTION id gt This error indicates that there were FUNCTIONs or IMPLICITs that referenced other FUNCTIONS or IMPLICITS and that the depth of the nested invocation exceeded the maximum allowed The default is n216 for workstations and n 8 for the IBM PC FUNCTION IMPLICIT NESTING
18. 15926 MU 4 P comment I When a comment spans more than one line a capital X appears in the log file for each of the lines that begins with the continuation of a comment For example 0001 0002 X This is a very very very 0003 X long comment 0004 X 0005 12 2 1 5 Quoted SURE statement Statements in the ASSIST input file that are put inside quotation marks are copied into the SURE input file and are not otherwise processed by ASSIST For example INPUT DELTA FOO 1 TO 10 BY 2 THIS IS A LONG COMMENT TO BE INCLUDED IN THE SURE INPUT FILE The statements in quotation marks need not be followed by a semicolon for ASSIST However for the statement to be followed by a semicolon in the SURE input file a semicolon must be put inside the quotation marks in the ASSIST input file These statements are put in the SURE input file in the sequence encountered Older versions of ASSIST before version 7 0 placed these statements before the constant definitions The new version gives the user more control because constant and option 13 definitions can now be mixed with quoted SURE statements and they will be placed in the model out put file in the same order in which they were typed into the input file 12 2 1 6 SPACE statement The SPACE statement is used to specify the state space on which the model is defined The state space is defined by an n dimensional vector where each
19. 3 17 94 9 46 50 a m ASSIST 7 1 NASA LaRC Page 1 0001 LAMBDA 1 e 4 0002 NP 3 0003 51 0004 SPACE NW 0 NP 0005 START NP 0006 0007 IF NW gt 0 THEN 0008 TRANTO NW BY NW LAMBDA 0009 ENDIF 0010 0011 DEATHIF NP NW gt NW PARSING TIME 0 14 sec RULE GENERATIO IME 0 00 sec NUMBER OF STATES IN MODEL 3 NUMBER OF TRANSITIONS IN MODEL 2 1 DEATH STATES AGGREGATED INTO STATE 1 17 4 Piping Model to Standard Output The pipe option is used on UNIX systems to write the model to standard output so that it can be piped directly to SURE For example to process the input file foo ast and pipe the model directly to SURE for solution use the command assist foo pipe sure gt sureout When the pipe option is specified dialog which normally appears on the standard output is redirected to the standard error The nostats option can be used together with the pipe option to suppress the printing of ASSIST statistics This is useful when the output from SURE is to come directly to standard output and would otherwise be scrambled with the standard error file statistics from ASSIST For example assist foo pipe nostats sure The model output from ASSIST should not be piped directly to SURE unless all errors and warnings have been fixed If this is done the standard output from SURE will b
20. Approved REPORT DOCUMENTATION PAGE Public reporting burden for this collection of information is estimated to average 1 hour per response including the time for reviewing instructions searching existing data sources gathering and maintaining the data needed and completing and reviewing the collection of information Send comments regarding this burden estimate or any other aspect of this collection of information including suggestions for reducing this burden to Washington Headquarters Services Directorate for Information Operations and Reports 1215 Jefferson Davis Highway Suite 1204 Arlington VA 22202 4302 and to the Office of Management and Budget Paperwork Reduction Project 0704 0188 Washington DC 20503 1 AGENCY USE ONLY Leave blank 2 REPORT DATE 3 REPORT TYPE AND DATES COVERED August 1995 Technical Memorandum 4 TITLE AND SUBTITLE 5 FUNDING NUMBERS ASSIST User Manual WU 505 64 10 07 6 AUTHOR S Sally C Johnson and David P Boerschlein 7 PERFORMING ORGANIZATION NAME S AND ADDRESS ES 8 PERFORMING ORGANIZATION REPORT NUMBER NASA Langley Research Center Hampton VA 23681 0001 L17407 9 SPONSORING MONITORING AGENCY NAME S AND ADDRESS ES 10 SPONSORING MONITORING AGENCY REPORT NUMBER National Aeronautics and Space Administration NASA TM 4592 Washington DC 20546 0001 P 0 11 SUPPLEMENTARY NOTES Johnson Langley Research Center Hampton VA Boerschlein Lockheed Engineering amp Sciences Company Hampto
21. Each TRANTO rule is then evaluated for the nondeath state If the condi tion expression of the TRANTO rule evaluates as true for the current state the destination expression is used to determine the state space variable values of the destination state If the destination state has not been defined in the model the new state is added to the ready set of states to be processed The transi tion rate is determined from the rate expression and the transition description is printed to the model file When all TRANTO rules have been applied to it the state is removed from the ready set When the ready set is empty all possible paths terminate in death states and model building is complete By default all death states are aggregated or lumped ONEDEATH ON according to the first DEATHIF statement to which the state conformed If the user sets ONEDEATH OFF then all distinct death states are kept in the model Note that the ready list is a subset of all state nodes that have been processed up to any given point All state nodes that have been processed must remain in memory because ASSIST must check each new destination state to see if it has already been processed There are typically many different paths to each model state States are processed only once 29 The following is a pseudo code version of the algorithm used to generate the model FUNC no stat te that fast number searc
22. LEVEL OVERFLOW SPECIFY NEST OPTION id This error is the VMS equivalent of the previous error IDENTIFIER ALREADY DEFINED gt This error indicates that the user tried to redefine an identifier that had been defined previously The identifier may have been used in the parameter list for a FUNCTION or IMPLICIT definition statement and is now being defined as a constant Once an identifier is used in a parameter list it may be reused in another parameter list or as a FOR index but it may not be reused as a named constant See sections 3 2 4 3 2 3 and 12 2 7 3 for descriptions of the respective statements IDENTIFIER EXPECTED token gt This error indicates that something other than an identifier was encountered when the syntax for ASSIST requires an identifier The token found instead of the identifier is echoed IDENTIFIER NOT DEFINED id gt This error indicates that an identifier was used before it was defined IDENTIFIER OR LITERAL EXPECTED token gt This error indicates that something other than an identifier or literal was encountered when the syntax for ASSIST requires an identifier or literal The token found instead of the identifier or lit eral is echoed The user probably has two arithmetic operations in a row without an item between them For example X 3 is illegal because there is nothing between the
23. Many Triads With Pool of Spares 0 0 ee ec m 39 7 3 Quad With Transient Fals aae n aa o aee een E E 40 7 4 Monitored Sensor Failure 2 0 arana a a i E aE E ONA 41 7 5 Two Triads With Three Power Supplies 0 0 eee 42 7 6 Triad With Intermittent Faults 0 cece eee nee 44 7 7 Degradable Triad With Intermittent Faults 0 0 0 eee eee 46 7 8 Triad With Hot Warm Cold Spares sse 47 8 Command Line Parameters and Options 50 8 1 Controlling Error Warning Limits leeeeeeeeeeeeeee I ae 51 8 2 Changing Allowable Input Line Width lleeeeeeeeeee eee 51 8 3 Generating Identifier Cross Reference Map 0 0 cece eee eee 51 8 4 Piping Model to Standard Output 0 0 urarena eere 52 8 5 B tch Mode sione Roe iit eh in anniv a nde ba a ea eon ded estan 52 8 6 Controlling Printing of Warning Messages 0 eee eee eee eee eee 52 9 Concluding Remarks ssri oe Rer NR NR Oe ee ihe E E RE 52 Appendix A Expression Precedence 0 0 eee nren 54 Appendix B BNF Language Description 0 cece cen eee ences 56 Appendix C Errors Warnings Detected 0 0 cece eee eee nes 65 Appendix D Debugging ASSIST Input Files sls 91 Appendix E Command Line Options 0 cece hm 93 REPETENCES 22 6 rl sey eae ee ee a a A eS ee EIS EM 96 List of Tables Table 1 Truth Table for AND Conjunction 0 00 cece ee 5 Table 2 Truth Table
24. NS BY FAST 1 NFS NS NFP J DELTA Replace failed processor with working spare IF NFS gt 0 TRANTO NS NFS BY FAST NFS NS NFP J DELTA Replace failed processor with failed spare ELSE TRANTO NP J 0 NFP J 0 NS NP J NFP J NT BY FAST OMEGA Break up a failed triad when no spares available ENDIF DIF ti jw EATHIF 2 NFP J gt NP J AND NP J gt 0 Two faults in an active triad is system failure ENDFOR DEATHIF NT 0 System failure by exhaustion Since variable sized arrays were used a system with any number of initial triads may be modeled by setting the constant N_TRIADS As shown in the example above the number of initial spares is set with the constant N SPARES Table 10 shows that changing these two constants has a dramatic effect on the number of states in the generated model Table 10 Number of Model States for Various Initial Configurations With ONEDEATH OFF Number of model states for spares numbering Number of triads 0 1 2 3 4 5 1 4 10 19 31 46 64 2 45 61 85 117 157 205 3 219 259 319 399 499 619 4 889 985 1129 1321 1561 1849 5 3323 3547 3883 4331 4891 5563 16 3 Quad With Transient Faults A quad architecture with both permanent and transient faults is modeled in this example The sys tem behavior is as follows Permanent faults arrive at rate P 2 Transie
25. The model that is generated for this example contains 15 states and 20 transitions This ASSIST input file could be used to model a triad a quintet or any number of starting processors by changing the constant NP With 7 initial processors the model contains 50 states and 100 transitions 16 4 Monitored Sensor Failure A triad of monitored sensors is modeled in this example Faulty sensors are detected by majority voting If half the active sensors are faulty and the vote could produce a tie the monitors are used to detect which sensor is faulty Detection using the monitors has imperfect coverage The system behav ior is as follows 1 Sensors fail at rate s 2 Monitors fail at rate ue 3 If a majority of the sensors are nonfaulty a failed sensor is removed with a mean time of y and a standard deviation of o When majority voting is used for fault detection the probability of detect ing the correct sensor as faulty is 1 4 If exactly half the sensors are faulty a sensor is removed with a mean time of u and a standard deviation of c In this case the probability that the nonfaulty sensor was the one removed is 0 98 5 The system fails if the majority of sensors fail or if half the sensors fail and the number of moni tors is less than the number of sensors 41 The ASSIST input file to describe this system is as follows
26. VARIABLE EXPECTED token gt This error indicates that something other than a state space variable was encountered when the syntax for ASSIST requires a state space variable The token found instead of the state space vari able is echoed It usually occurs in the destination clause of a TRANTO during an illegal attempt to change the value of an identifier other than a state space variable STATE SPACE VARIABLE VALUE IS OUT OF RANGE num min to max This error indicates that during rule generation or during the parsing of a START statement a state space variable took on a value outside the range declared to be legal in the SPACE statement Be sure to check for consistency between the SPACE START and all TRANTO statements See sections 3 2 1 6 3 2 6 and 3 2 7 1 for further details STATEMENT EXPECTED token gt This error indicates that ASSIST was looking for the beginning of a statement but found the token echoed to the right of the colon All statements must begin with a reserved word except for the SURE statement which begins with a quote and the constant definition statement which begins with an identifier followed by an equals sign STATEMENT NOT VALID IN THIS SECTION constant definition of id lt expr gt gt Once the rule section begins the user may no longer define any more constants because the rules are applied iteratively to all model states and are by def
27. and 26 transitions 16 5 Two Triads With Three Power Supplies This example has two computer triads and one triad of power supplies that are connected so that one computer in each triad is connected to each power supply Thus if a power supply fails one computer in each triad fails Because of the complex failure dependencies this is a difficult system to model The usual method of using state space variables to represent the number of failed computers in each triad is insufficient because which computers have failed is also important state information One way to model this system is to use the state space variables as flags to indicate the failure of each computer and power supply in the system This method uses a large number of state space variables but the sys tem can be described using only a few simple TRANTO statements The large number of state space variables however leads to an unnecessarily complex semi Markov model The ASSIST input file is as follows 2 TRIADS OF COMPUTERS WITH 1 TRIAD OF POWER SUPPLIES CONNECTED SUCH THAT 1 COMPUTER IN EACH TRIAD IS CONNECTED TO EACH POWER SUPPLY THUS IF A POWER SUPPLY FAILS THEN ONE COMPUTER IN EACH TRIAD FAILS THE SYSTEM FAILS IF EITHER TRIAD OF COMPUTERS FAILS 42 a LAM PS 1E 6 Failure rate of power supplies
28. and are not reported unless WARN ZALL is specified on the VMS com mand line or WARN ALL is specified on the UNIX command line Some potential problems that are detected are reported as both errors and warnings depending upon the context in which the prob lems were encountered Note that after detecting an error in a statement ASSIST makes a best guess attempt to recover enough so that it can continue to find more errors without generating too many extraneous error mes sages Sometimes it is not possible to do this If a line contains several error messages and most of them do not seem to apply fix the ones that do apply The other errors especially when they follow the ones that do apply will probably disappear when the fixes are made C 1 Listing of Detected Errors An alphabetical listing of all error messages follows AN INTEGER EXPRESSION MUST PRECEDE THE WORD OF token gt This error indicates that something other than an integer expression preceded the word OF dur ing repetition usually in a START statement It is usually caused by the presence of a real number but can also be caused by an ill formed expression ARCCOS X ARGUMENT MUST BE 1 0 lt X lt 1 0 real ABS 1 0 expression on line linenumber gt This error indicates that during rule generation an expression that was passed to the built in func tion ARCCOS evaluated to real a number
29. component of the vector is called a state space variable and defines an attribute of the system being modeled Attributes can be whatever is convenient Examples might include such things as the number of components the number of working components the number of spare components the number of active failed components the number with benign faults aflag for each component indicating whether it is working The syntax of the SPACE statement is EN SPACE lt space picture gt 3 The syntax of a lt space picture gt is lt space item gt space item The syntax of a lt space item gt is lt ident gt or ident ARRAY lt expr gt expr OF lt expr gt lt expr gt or lt ident gt ARRAY expe lt expr gt OF BOOLEAN or lt space picture gt The ellipsis between the square brackets following the word ARRAY denotes the value range over which an index into the array can vary The ellipses that are shown immediately after the colon for a scalar and immediately after the word OF for an array denote the value range over which the state space variable can vary i e the value range that legally can be stored for the scalar array during the generation phase Any values between 0 and 32767 are allowed for subscripts or ranges The syntax for the SPACE statement is recursive because a space picture can contain a nested space picture within it This allows
30. ever exceeds this value then ASSIST will quit processing the input file immediately after printing an appropri ate error message The default is a maximum of 40 warnings allowed per input file bc nnn Specifies the bucket count for the rule generation state hashing algorithm If rule generation is taking a long time because of identifier hash clashes this value can be adjusted The default bucket count is 1009 bi nnn Specifies the bucket increment The bucket increment controls how many addi tional state buckets will be allocated at a time when the system runs out of buckets bw nnn Specifies the bucket width i e the number of states that will fit in a single link of the linked list for each bucket for the rule generation state hashing algorithm If rule generation is taking a long time because of identifier hash clashes this value can be adjusted The default bucket width is 5 lp nnn Specifies the number of lines per page on the log file The default is 58 lines maxi mum per page on the log file i nnn Specifies the maximum number of identifiers that can be held in the identifier table The default is a maximum of 400 unique identifier names in the table for most systems 200 on the IBM PC n nnn Specifies the maximum number of literal values that can be held in the identifier table Note that 6 0 and 6 00 are considered as two different entries in the table so that
31. f ig ih i jj k 1 m n 0 N w lt digit gt ident char identifier ident rest unsigned integer value ao 4 2 H m z Ne 0 1 5 6 letter digit under dollar letter letter ident rest ident char lt ident char gt ident rest digit digit unsigned integer value unsigned real value lt unsigned integer value gt unsigned integer value unsigned integer value unsigned integer value exponent value exponent value XE char lt sign op gt unsigned integer value lt E char gt unsigned integer value named constant identifier lt state space var gt lt identifier gt index variable identifier The C OPTION statement can be repeated but will usually precede any other statements This syntax is obsolete at revision 7 0 its use will result in a warning message All identifiers with dollar signs are reserved by the ASSIST language 8 Although lower and upper bounds can take on values between 0 and 32767 their difference must be no more than 255 64 Appendix C Errors Warnings Detected The ASSIST language checks for errors in the input file Appropriate error or warning messages are displayed depending upon the severity of the problem detected The following conditions are tested Some are petty warnings
32. fast trans FOR all recov ute new state new state print the increment ENDFOR all states on ready list th state flagged as dea ition counter ery fast number lt call transition to fast transitio CO Z TRANTO s 30 PROC xisting states IE S t AND h state number number THI Ei zZ state number add the state to the ready list t variable values trimming is on THI compute dependent variables referenced in TRANTO section Start state number call PROC LOOP THEN ero DO ESS start state NORMAL N A error EN transitions directly to death state suited to trimming ESS new state NORMAL FAST error the model file n counter IF trimming is on THE set slow transition counter to zero FOR all non recovery slow TRANTO s DO compute new state IF fast transition counter 0 THEN new state number call PROCESS new state TRIM SLOW error ELSE new state number call PROCESS new state NORMAL SLOW error ENDIF print the transition to the model file ENDFOR Er Iz wn E set slow transition counter to zero FOR all non recovery slow TRANTO s DO compute new state new state number call PROCESS new state NORMAL N A print the transition to the model file ENDFOR ENDIF ENDIF print warning if no transitions out of a non death stat
33. following is an example SPACE DIM1 2 4 DIM2 3 5 DEATHIF DIM1 4 OR DIM2 3 This statement defines 4 3 4 4 4 5 2 3 and 3 3 as death states In general the syntax is DEATHIF lt condition gt The lt condition gt is a Boolean expression with optional parentheses For example DEATHIF NWP lt NFP death if no longer majority working DEATHIF 2 NWP I lt NP I AND NT 1 death if last triad fails Unless the ONEDEATH option is turned off explicitly in the input file generated death states will be aggregated according to which DEATHIF statement they satisfy See the description of the ONEDEATH option section 12 2 1 2 for a complete description of this feature 12 2 7 6 PRUNEIF statement Because systems with numerous components exhibit a combinatorial explosion of states the conservative pruning method can be used to limit the number of model states and consequently can greatly decrease the solution time as well as the hardware memory required for solution A system model with many components usually has many long paths consisting of one or two fail ures of each component type before system failure is reached Because the occurrence of so many fail ures is unlikely during a short mission these long paths typically contribute insignificantly to system failure probability The dominant system failure modes are typically the s
34. for OR Conjunction 0 cece II 5 Table 3 Truth Table for XOR Conjunction 0 0 cece e 5 Table 4 Truth Table for NOT Conjunction 2 0 0 cent ene eae 5 Table 5 Built in Math Functions 0 0 00 cece cece cece eee s 7 Table 6 Built in Trigonometric Functions 7 Table 7 Built in Combinatorial Functions 0 0 0 cece eee eee eens 8 Table 8 Built in Array List Functions 8 Table 9 Bits Required to Pack a State Space Variable 0 0 0 cee eee ee eee 15 Table 10 Number of Model States for Various Initial Configurations With ONEDEATH OFF 40 Table A1 Order of Precedence Used by ASSIST for Mathematical Expressions 54 Table C1 ASSIST Warning Levels 0c eee ee ee eee Seb ee eae Rh mede 87 iv List of Figures Figure 1 Semi Markov triad model SURE state numbers 00 0 c eee eens 2 Figure 2 Semi Markov triad model ASSIST state numbers 0 0 0 e cece eee 3 Figure 3 Data file flow in ASSIST 0 ccc cence ences 32 Figure 4 Semi Markov triad model with cold spares ASSIST state numbers 37 Figure 5 Semi Markov triad model with cold spares SURE state numbers 38 Abstract Semi Markov models can be used to analyze the reliability of virtu ally any fault tolerant system However the process of delineating all the states and transitions in the model of a complex system can be dev astating
35. for states such as 6 0 2 8 6 0 4 1 4 TRUE 8 FALSE 4 2 2 r 2 2 This feature can be useful for analysis and for checking correctness when a model contains a large number of state space variables Long lists of state space variable values in the model file comments can be difficult to read unless some subgrouping is done Consistent nesting of the state space is enforced between the SPACE START and TRANTO statements i e if nested parentheses are used in the SPACE statement they must also be used in the START statement and whenever the entire state space is enumerated in a TRANTO statement Nested parentheses have no actual effect on the model generation 14 Some examples of SPACE statements follow In these examples NSI_pool is a constant that must be defined prior to the SPACE statement to represent the number of spares initially in the spare pool SPACE NW triad 0 3 Count of working in triad NFA triad 0 3 Count of active failed in triad NFB triad 0 3 Count of benign failed in triad NCF 0 9 Number of component failures for PRUNEIF SPACE W triad ARRAY 0 3 OF BOOLEAN Each working in triad NS pool 0 NSI pool Spares count COLD pool pool NCF 0 3 NSI pool Number of component failures for PRUNEIF Each variable with an unspecified range has the default range fr
36. for very few states an IMPLICIT may be more efficient than a VARIABLE Another difference is that a VARIABLE can define an array whereas an IMPLICIT cannot The syntax for the VARIABLE statement is VARIABLE lt identifier gt lt state space variable list gt BOOLEAN lt definition clause gt 3 where a definition clause defines either a scalar or an array Its syntax is lt expr gt or lt gt oF lt expr gt lt gt oF lt expr gt h or ARRAY lt gt OF expr lt gt OF expr The lt state space variable list gt is made up of one or more state space variable name identifiers separated by commas The identifiers must already have been defined in a SPACE statement All state space vari ables that are referenced in the definition clause of a VARIABLE must be listed in the state space vari able list The lt definition clause gt of the VARIABLE definition is the expression defining the VARIABLE as either a variable or an array which is dependent upon the state space Named constants and reserved words may be freely referenced to the right of the equals sign and must not be specified with the state space variables The VARIABLE may be referenced in TRANTO DEATHIF PRUNEIF ASSERT IF or FOR state ments or in later VARIABLE IMPLICIT or FUNCTION definitions in exactly
37. goes benign KKK KKK KKK KEK KKK KKK KKK KKK ck kck ck ck ck kk KKK KKK KKK KEK KKK KKK KKK KKK ck ck ck ck ck ck kk KK kk MISC DEATH amp PRUNE kk KK KKK KKK KKK KKK KKK KKK KKK KKK KK KKK KK KKK KKK KKK KEK KKK KKK KKK KKK ck ck ck ck ck ck KK EATHIF TFA_triad gt TWA_triad 45 x Intermittent fault arrival Benign fault goes active triad A B triad NFA triad Total active in triad FB triad Total active working in triad 16 7 Degradable Triad With Intermittent Faults The next example is a degradable triad subject to intermittent faults This triad has three processors with intermittent fault arrival rates of X I When an intermittent fault arrives it is assumed to be in an active state i e it is actively producing errors After arrival intermittent faults change to a benign state at fast exponential rate B and change to an active state again at fast exponential rate Active processors that are faulty are removed from the system at fast exponential rate pp A solution using STEM or PAWS is necessary because the SURE program cannot handle the fast loops in this model kCkCkckckckckckckckckckckckckck ck ck ckck ck ck ck ko k kk kCckCkckckckckckckckck ck ckckckckck ckckck ck ck ck kc k kk aK kK KEK RATE CONSTANTS RM aK kK KKK KKK KKK KKK KK KKK KK KKK ck kc k KK KKK KKK KK KKK KKK KKK ck c
38. input line The wl option controls the maximum cumulative number of warnings allowed throughout the entire input file Examples are assist foo el 80 assist foo 1 100 w1 21000 lel 10 1w1 10 Defaults are assist foo 1 40 wl1 40 lel 5 lwl 5 17 2 Changing Allowable Input Line Width The wid option changes the allowable length of an input line The default width is 79 The num ber 79 was chosen because input lines are echoed to the terminal when an error occurs and because some terminals wrap truncate with column 80 The value can be changed as illustrated in the example assist foo wid 133 17 3 Generating Identifier Cross Reference Map The xref synonymous with map option causes inclusion of an identifier cross reference map in the log log file The map follows the input listing and includes the line declared in line s defined given a value in and lines referenced in Also referenced are matching ELSE and ENDIF and match ing ENDFOR key words In a cross reference listing DCL stands for declared and indicates the line on which the item was declared SET indicates the line s on which the item took on a value and USE indicates the line s on which the item was referenced used The following shows the syntax of input line references lt line number gt lt column number gt The following log file was produced with xref sysl ast
39. of error reporting are requested GI THIS STATEMENT IS INDEPENDENT OF FOR INDEX id gt This warning indicates to the user that the specified statement does not depend upon the FOR loop index to the right of the colon The statement could therefore safely be moved out of the FOR con struct for clarity and simplicity The user should check the statement to confirm that no intended references to the FOR index were omitted This warning message appears when two or more levels of error reporting are requested VALUE ASSIGNED TWICE IN SAME TRANTO FOR THIS STATE SPACE VARIABLE id This warning indicates that the state space variable was adjusted twice in the same TRANTO as in TRANTO NWP NWP BY The net effect of the transition would be to ignore the first adjustment and use only the final one In the example the NWP would be ignored and the NWP would be used because the decrementing appeared later in the statement than did the incrementing This serious warning message appears when 1 or more levels of error reporting are requested In some instances as in the case of array state space variables with variable subscripts the warning is minor and appears when three or more levels of warning are requested 90 Appendix D Debugging ASSIST Input Files The most cautious user will occasionally mistype something in an ASSIST input file Usually gen
40. parameter list the IMPLICIT is invoked by its name alone The following example illustrates the definition and invoca tion of IMPLICITs SPACE NWP ARRAY 1 5 OF 0 3 Number working in each of five triads IMPLICIT NFP NWP IX 3 NWP IX Number failed in each triad IMPLICIT TOTALW NWP SUM NWP IMPLICIT TOTALF NWP 3 5 TOTALW 16 FOR III IN 1 5 IF NFP III gt 0 TRANTO NWP III 0 BY 1 E 5 ENDFOR DEATHIF TOTALF gt 6 In the above example the IMPLICIT function NFP is declared a function of the state space vari able NWP and the parameter IX The value of NFP is computed as three minus the current number of working processors in the triad corresponding to the passed parameter The IMPLICIT function TOTALW is also a function of the state space variable NWP but has no parameters This function value is computed as the number of working processors in all five triads The IMPLICIT function TOTALF is also a function of the state space variable NWP but has no parameters The body of TOTALF refer ences the value of IMPLICIT function TOTALW Since TOTALW is computed based upon the state space variable NWP then NWP must be listed in the state space variable list for TOTALF even though it is only referenced indirectly When NF P is referenced in the IF the value of III is passed as a param eter to sati
41. parsing an expression that must evaluate to an integer evaluated to a real or Boolean It probably means that the value following the concatenation operation was not an integer INTEGER MODULO BY ZERO int MOD int expression on line linenumber gt This error indicates that during rule generation the user tried to divide by zero in order to obtain the integer remainder This is illegal do not do it INTERNAL ERROR PLEASE CONTACT COMPILER SUPPORT unknown type for value to memory gt This error indicates a problem so serious that ASSIST could not deal with it Try fixing all other errors first INTERNAL ERROR PLEASE CONTACT COMPILER SUPPORT Already has a type lookup ident This error indicates a problem so serious that ASSIST could not deal with it Try fixing all other errors first INTERNAL ERROR PLEASE CONTACT COMPILER SUPPORT Attempt to evaluate an expression in error gt This error indicates a problem so serious that ASSIST could not deal with it Try fixing all other errors first 73 INTERNAL ERROR PLEASE CONTACT COMPILER SUPPORT Attempt to evaluate the empty expression gt This error indicates a problem so serious that ASSIST could not deal with it Try fixing all other errors first INTERNAL ERROR PLEASE CONTACT COMPILER SUPPORT BAD BINARY OP gt This error indicates a problem so serious that A
42. that would affect disk drive access CANNOT RAISE A NEGATIVE NUMBER TO A REAL POWER real real expression on line linenumber gt This error indicates that during rule generation an attempt was made to raise a negative number to a real power If the power is something like 2 0 then it should be changed to 2 COLON EXPECTED token gt This error indicates that something other than a colon was encountered when the syntax for ASSIST requires a colon The token found instead of the colon is echoed COMMA EXPECTED token gt This error indicates that something other than a comma was encountered when the syntax for ASSIST requires a comma The token found instead of the comma is echoed COMMA EXPECTED token FUNCTION func This error indicates that something other than a comma was encountered in the parameter list for a FUNCTION when the syntax for ASSIST requires a comma The token found instead of the comma is echoed COMMA EXPECTED token IMPLICIT impl This error indicates that something other than a comma was encountered in the parameter list for an IMPLICIT when the syntax for ASSIST requires a comma The token found instead of the comma is echoed COMMA EXPECTED func REQUIRES 1 num PARAMETERS AND NO FEWER gt This error indicat
43. the identifier that was too long This warning message appears when two or more levels of error reporting are requested INPUT LINE TOO LONG gt This warning indicates that an input line has been truncated and that part of the information from the end of the line was thrown away This almost always results in the propagation of at least one error unless of course the truncated text was just part of a comment This serious warning mes sage appears when one or more levels of error reporting are requested I INTERNAL ERROR PLEASE CONTACT COMPILER SUPPORT token gt As a warning this message indicates that ASSIST could not anticipate potential problems which are normally checked If the standard error file reads Algorithm to check for TRANTO destina tion duplication errors flushed in qq parse space expr list then ASSIST could not fully check for as many errors as it could have if the algorithm had not been flushed The gener ated model is probably correct but the user should check it more thoroughly This serious warning message appears when one or more levels of error reporting are requested LITERAL CHARACTER STRING TRUNCATED sfring This warning indicates that the text of a SURE statement or an INPUT prompt had to be truncated because it was too long This serious warning message appears when one or more levels of error reporting are requested 88 MISSING TOKEN INSERTED BY PARSER gt Thi
44. the limit is being increased NUMBER OF WARNINGS EXCEEDS LIMIT OF 40 gt This error indicates that the maximum number of warnings per input file has been exceeded ASSIST will therefore no longer continue parsing the input file for additional errors warnings The limit can be increased with the wl command line option as in wl 50 The warnings will ulti mately have to be fixed anyway so it is good practice to start correcting them even if the limit is being increased I I NUMBER OF WARNINGS LINE EXCEEDS LIMIT OF 3 gt This error indicates that the maximum number of warnings per line has been exceeded ASSIST will therefore no longer continue parsing the input file for additional errors warnings The limit can be increased with the lwl command line option as in IwIz10 The warnings will ulti mately have to be fixed anyway so it is good practice to start correcting them even if the limit is being increased NUMBER TOO LONG OR VALUE TOO BIG inf IS THE COMPUTED VALUE This error indicates that a number was computed for a constant expression and it was larger than allowed in its context This error usually indicates that one of the bounds on a state space variable in the SPACE statement is larger than 32767 or the repetition count to the left of the OF key word in a START statement is larger than 32767 State space variables can have values as large as 32767 but the difference
45. the same manner as a constant would be referenced The VARIABLE is referenced in the same way as a constant would be Square brackets are used when the VARIABLE is an array The following example illustrates the defini tion and use of VARIABLEs SPACE NWP ARRAY 1 5 OF 0 3 Number working in each of five triads VARIABLE NFP NWP T NWP NWP NWP NWP NWP 5 Number failed in each triad SUM NWP 3 5 TOTALW WWW CO CO AUNE yas VARIABLE TOTALW NWP VARIABLE TOTALF NWP FOR III IN 1 5 IF NFP III 0 TRANTO NWP III 0 BY 1 E 5 ENDFOR DEATHIF TOTALF gt 6 In the example above the variable NFP is dependent upon the state space variable NWP and is an array with five elements Each element value is computed as three minus the current number of work ing processors in the triad corresponding to the array index The variable TOTALW is also dependent upon the state space variable NWP Its value is computed as the total number of working processors in all five triads The variable TOTALF is also dependent upon the state space variable NWP The defini tion of TOTALF references the value of variable TOTALW Since TOTALW is computed based upon the state space variable NWP then NWP must be listed in the state space varia
46. their longhand counterparts The first of these requires three operations one to fetch NFP one to fetch the number 1 and one to compute the sum The second requires two operations one to fetch and one to increment A seemingly minor speedup of an operation that is per formed once for every transition can result in a noticeable speedup in the generation of a very large model Only state space variables may be changed in the destination clause of a TRANTO statement Because IMPLICIT functions are typically used to define dependent variables that are IMPLICIT functions of the state space one might be tempted to change them in a destination clause This practice however is not allowed For example the following would not be valid SPACE NP 0 5 NWP 0 5 IMPLICIT NFP NP NWP NP NWP TRANTO NFP BY NWP LAMBDA The transition should be correctly entered as TRANTO NWP BY NWP LAMBDA to increment the state space variable itself rather than the IMPLICIT function name Rate expression The expression following the BY key word indicates the rate of the transition to be added to the model This expression may contain FOR index variables and state space variables as well as constants and arithmetic operations The rate expression is the only expression in which real con stants may be used There are three ways of expressing a rate in the SURE input language that are sup ported in
47. triads are handled The only significant model changes are a new transition type and a new type of system failure The new transi tion is the breakup of a triad when it fails and there are no spares System failure by exhaustion must also be modeled which requires an extra state space variable and a new DI HATH F statement MULTIPLE TRIADS WITH POOL OF SPARES T INPUT N_TRIADS Number of triads initially INPUT N_SPARES Number of spares _PROCS 3 Number of active processors per triad LAMBDA_P 1E 4 Failure rate of active processors LAMBDA S 1E 5 Failure rate of cold spare processors DELTA 3 6E3 Reconfiguration rate to switch in spare OMEGA 5 153 Reconfiguration rate to break up a triad SPACE NP ARRAY 1 N_TRIADS OF 0 N_PROCS processors each triad NFP ARRAY 1 N_TRIADS OF 0 N_PROCS active each triad NS Number of spare processors NFS Number of failed spare processors NT O N_TRIADS Number of non failed triads 39 START N_TRIADS OF N_PROCS N_TRIADS OF O0 N_SPARES 0 N TRIADS IF NS gt NFS TRANTO NFS NFS 1 BY NS LAMBDA 9 Spare failure FOR J IN 1 N_TRIADS IF NP J gt NFP J TRANTO NFP J BY NP J NFP J LAMBDA P Active processor failure H tj NFP J 0 THEN IF NS gt 0 THE IF NS gt NFS TRANTO NFP J
48. 02
49. 0X KKK KKK KK KKK KKK KKK ck ckck ck ck KK KKK KKK KKK KKK KKK KK KKK ck ckck ck ck ck ck ck kk SPACE CONSTANTS o KKK KKK KKK KKK ckckckckck ckckck ck ck ck kk kk KKK KKK KKK KKK ckckckck ck ckckck ck ck ck kk kk Redundancy count for triad Initial pool size for hot Initial pool size for warm Initial pool size for cold Total number of components initially Arrival rate of permanent fault for triad Rate to reconfigure hot spare into triad Rate to reconfigure warm spare into triad Rate to reconfigure cold spare into triad 2e 4 Arrival rate of permanent hot spare faults 0e 8 Arrival rate of permanent warm spare faults KKK T KKK KKK KKK KKK KKK KKK KKK ck ckckck ck ck ck ck ck ck ck ck k KKK KKK KKK KEK KKK KKK KKK KKK ck kckck ck ck kk KKK KKK KKK KEK KKK KKK KKK KKK KKK ck ck ck ck k KKK KKK KKK KKK KK KKK KKK KKK KKK ck ck ck kk NI triad NSI hot NSI hot NSI warm NSI warm NSI cold OoOOooOoo0o0oc0 triad NW triad riad NW triad triad NW triad riad riad NI triad STATE SPACE DEFINED o6 x F 0X X IMPLICIT NS hot NWS hot NFS hot IMPLICIT PRW_ IMPLICIT PRE hot NWS hot NFS hot hot NWS hot NFS hot Count of working in triad Working spares count HOT pool hot Failed spares count HOT pool hot Working spar
50. 6 for the IBM PC The default is e 100 for workstations and e 50 for the IBM PC The default is p 64 for workstations and p 32 for the IBM PC The default is rule24096 for workstations and rule 1024 for the IBM PC INSUFFICIENT MEMORY FOR PARSE PHASE Identifier table gt This error indicates that the total table size was bigger than ASSIST will allocate This error always arises from large values for the i and n options Try decreasing the value specified on the command line for either or both of these options The default is i 400 for workstations and i 200 for the IBM PC The default is n 200 for workstations and n 50 for the IBM PC INSUFFICIENT MEMORY FOR PARSE PHASE astparse storage gt This error indicates that the total table size was bigger than ASSIST will allocate This error always arises from large values for the e o p nest pic and rule options Try decreasing the value specified on the command line for one or more of these options The default is pic 100 for workstations and pic 100 for the IBM PC The default is o 100 for workstations and 0 50 for the IBM PC The default is nest 16 for workstations and nestz8 for the IBM PC The default is n 200 for workstations and n 50 for the IBM PC The default is e 100 for workstations and e 50 for the IBM PC The default is p 64 for workstations and p 32 for the IBM PC The default is r
51. ABLE 175 0 38 24 T1235 5 ju 29 lX 99 94 us 29 44 66 102 13 12 1 6 Ranges A range specifies a contiguous sequence of whole numbers positive integers The syntax of a range is expression expression The ellipsis indicates a value range beginning with the left value and ending with the right value inclusively Thus 5 9 specifies the numbers 5 6 7 8 9 whereas 5 9 specifies the numbers 5 and 9 6 12 1 7 Repetition The ASSIST language allows the use of repetition in several places For example instead of typing 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 one can merely type I3 OE 0 9 ORS 3 12 1 8 Built in Functions Several mathematical trigonometric combinatorial list and array functions are available in the ASSIST language These functions can be used in expressions to compute numeric quantities based upon the parameter values passed to them For example the expression TRANTO NWP BY SQRT MU LAMBDA can be written to denote a transition to a new state at rate Ju A 12 1 8 1 Mathematical functions The mathematical functions are listed in table 5 Example uses of these mathematical functions are FOO SQRT FOOBAR FOO POW EXP 0 5 FOO LOGDIFF LN FOO FOOBAR ABSFOO PLUS 1 0 ABS FOO Table 5 Built in Math Functions Function Parameter type Result Description SQRT Real Real x EXP Real Real e LN Real Real In x ABS Real Real x
52. ANTO NFS hot BY FAST PRF hot DEL hot ELSE IF NS warm 0 THEN Try secondary spare pool warm next IF NWS warm gt 0 RANTO NWS warm NW triad t BY FAST PRW warm DEL warm IF NFS warm gt 0 RANTO NFS warm BY FAST PRF warm DEL warm ELSE IF NS cold 0 THEN Try tertiary spare pool cold last TRANTO NS cold NW triad BY FAST DEL cold ENDIF ENDIF ENDIF ENDIF Faults present Try primary spare pool hot first pd KKK KKK KKK KKK KKK ckckckck ck ck ck ck ck ck ck kk ck kk ck ckckckckckckockckckckck ckckckckck ck ck ck ck ck ck kc kc kk kk KKK E KK KKK KKK KKK KKK KKK KKK KKK ck ck ck ck ck KKK KK KKK KKK KKK KKK KK KKK KK ck ck ck ck ck ck ck ck kk SPARE POOL hot ASSERT NWS hot NFS hot lt NSI hot IF NWS hot gt 0 Arrival of permanent hot spare fault TRANTO NWS hot NFS hot BY NWS hot LAM hot kk Ck CkCckckck ck ckckckckckckckckckck ck ckckckck ck kck ck ck ck ck k kk ck CckCckckckckckckckckckckokckckck ck ckckckck ck ck ck ck ck ck ck k kk kck ORDEN SPARE POOL warm EE FJ KK K KK K KKK KKK KKK KKK KK KKK KKK KKK ck ck ck ck ck ck ck k KKK KKK KKK KEK KKK KKK KKK KKK KKK ck ck ck ck k 49 ASSER
53. ASSIST Slow transitions are specified by the transition rate The syntax is lt expr gt where lt expr gt is a real expression Fast transitions may be specified by two different methods White s method or the fast exponential method The syntax for White s method is mu sig frac gt where the three subexpressions define the following mu the conditional mean transition time sig the conditional standard deviation of the transition time the transition probability Ill lt frac gt All three parameters are real constants The third parameter is optional If omitted the transition probability is assumed to be 1 0 23 The syntax of the fast exponential rate expression is FAST lt rate gt where the rate is a real constant expression The SURE program automatically calculates the conditional moments from the unconditional rates given in this expression In the simple case with only one transi tion leaving a state the following three rate expressions are all equivalent BY lt 1 0 ALPHA 1 0 ALPHA gt BY lt 1 0 ALPHA 1 0 ALPHA 1 0 gt BY FAST ALPHA Spaces are not required around the punctuation They are present for clarity 12 2 7 2 Block IF construct The block IF construct at version ASSIST 7 0 relaxes most restric tions from prior versions Most noticeable is that FOR DEATHIF and other rules may now appear inside of block IF s as well as the TRANTO statements
54. FA_triad 0 NI_triad Count of working in triad 0 NI_triad Count of active failed in 0 NI_triad Count of benign failed in triad Redundancy count for triad Total number of components initially KKK KKK KKK KEK KKK KKK KKK KKK KKK ck ck ck kk KKK KKK KKK KEK KKK KKK KKK KKK ck ck ck ck ck ck kk KK KK K STATE SPACE DEFINED KKK KK KKK KKK KKK KEK KKK KKK KKK KKK ck ck ck KKK kk KKK KKK KKK KEK KKK KKK KKK KKK ck ck ck KKK kk FA triad NFA triad Total active failed in triad FA triad WA triad NW triad N NW triad NFB_triad A triad NW triad NF FA triad TWA triad Count of working in triad Count of active failed in triad Count of benign failed in triad IF NW triad gt 0 TRANTO NW triad NFA triad BY NW triad l IF NFB triad gt 0 TRANTO NFB triad T ALP 0 THE BY FAS L I triad triad BET t KKK KKK KKK KKK KK KKK KKK KKK ck ck ck ck ck ck ck k kk Ck CkCckckckckckckckckckckokckckck ck ckckckck ck kck ck ck ck kk kck kk COMPONENT triad KKK KK KKK KKK KKK KKK KKK KKK ck ckckckck ck KK KKK kk KKK KKK KKK KEK KKK KKK KKK KKK KKK ck ck ck kk RT TWA_triad TFA_triad NI_triad FA_triad Active Intermittent faults FB triad t riad Active fault
55. HIGHEST PRUNE LEVEL 2 03357e 17 0 000 SECS CPU TIME UTILIZED 38 exit The semi Markov model is shown in figures 9 and 10 The log file that is generated from executing ASSIST on this input file is 3 21 94 2 44 32 p m ASSIST 7 1 NASA LaRC Page 1 0001 o TRIAD WITH COLD SPARES 0002 0003 N_PROCS 3 Number of active processors 0004 N_SPARES 2 Number of spare processors 0005 LAMBDA P 1E 4 Failure rate of active processors 0006 LAMBDA S 1E 5 Failure rate of spare processors 0007 DELTA 3 6E3 Reconfiguration rate 0008 0009 SPACE NP O N PROCS Number of active processors 0010 NFP 0 N PROCS Number of failed active processors 0011 NS 0 N SPARES Number of spare processors 0012 NFS 0 N SPARES Number of failed spare processors 0013 0014 START N PROCS 0 N SPARES 0 0015 0016 DEATHIF 2 NFP gt NP 0017 0018 IF NP NFP RANTO NFP NFP 1 BY NP NFP LAMBDA P 0019 Active processor failure 0020 0021 IF NS NFS RANTO NFS NFS 1 BY NS LAMBDA S35 0022 Spare processor failure 0023 0024 IF NFP gt 0 AND NS gt 0 THEN 0025 IF NS gt NFS Replace failed processor with working spare 0026 RANTO NP NF
56. IABLE START ASSERT DEATHIF PRUNEIF PRUNIF TRANTO IF FOR ONEDEATH COMMENT ECHO TRIM name lt named constant gt const var def clause constant def clause BOOLEAN 57 constant def clause constant def clause double sub array lt sub array list gt single sub array option def stat lt INPUT stat gt lt SPACE stat gt function def impl function def dep variable def lt START stat gt lt ASSERT stat gt lt DEATHIF stat gt lt PRUNEIF stat gt lt TRANTO stat gt lt IF stat gt lt FOR stat gt lt expr gt j ARRAY lt expr list with of gt lt single sub array gt lt double sub array gt j lt sub array list gt lt single sub array gt lt single sub array gt lt single sub array gt lt sub array list gt lt expr list with of gt ONEDEATH lt flag status gt COMMENT lt flag status gt ECHO lt flag status gt TRIM lt flag status gt TRIM lt flag status gt WITH lt expr gt INPUT lt input list gt SPACE lt spac picture j FUNCTION lt function name gt lt function parm list lt expr gt IMPLICIT lt impl func name gt impl parm list lt expr gt IMPLICIT lt impl func name gt lt impl parm list gt index parm list lt expr gt VARIABLE lt impl func name gt impl parm list
57. LOW SPECIFY RULE OPTION id This error indicates that the user has more rule statements in series than allowed for at the nesting level where the error occurred There may be too many rules in the rule section or just too many rules between an IF and an ELSE or between a FOR and an ENDFOR The storage can be increased with the rule command line option The default is rule 4096 for workstations and rule 1024 for the IBM PC SCALAR EXPECTED arrayname op This error indicates that an array was found when a scalar was expected The user was attempting to perform arithmetic on a whole array instead of just on one element of the array The user proba bly forgot to specify a subscript in square brackets following the name of the array SCALAR EXPECTED arrayname gt This error indicates that an array was found when a scalar was expected The user probably forgot to specify a subscript in square brackets following the name of the array I SCOPE OF IDENTIFIER IS INACTIVE id This error indicates that an identifier was referenced but its use is no longer valid It usually occurs when a FOR index is referenced after the matching ENDFOR This error can also occur if an identi fier name is referenced without redefinition after it has already been used in the parameter list for the definition of a prior FUNCTION or IMPLICIT SCOPE OF IDENTIFIE
58. NASA Technical Memorandum 4592 ASSIST User Manual Sally C Johnson Langley Research Center e Hampton Virginia David P Boerschlein Lockheed Engineering amp Sciences Company e Hampton Virginia Mala August 1995 The use of trademarks or names of manufacturers in this report is for accurate reporting and does not constitute an official endorsement either expressed or implied of such products or manufacturers by the National Aeronautics and Space Administration Available electronically at the following URL address http techreports larc nasa gov ltrs ltrs html Printed copies available from the following NASA Center for AeroSpace Information National Technical Information Service NTIS 800 Elkridge Landing Road 5285 Port Royal Road Linthicum Heights MD 21090 2934 Springfield VA 22161 2171 301 621 0390 703 487 4650 Contents 12 Introduction 3 eor be Gehe Sethe Ge See en Ce oP ee ee OSD Se Re ee eS 1 2 Basic Concepts senes e e a ceeded ci iced ee d ogee ehh E deos air uite 2 3 Input E ngu age Syntax ix torp nemis RE pU bee ecquid ud VM 3 3 1 Language Building Blocks leleeeeeeeeee RI e 3 3 T 1 Identifiers o o oss n Rt Rt et RB ete OR EN ed e re OR e UN petet 3 311 2 Numeric EXpressions 5s aso eror hee pee po Pe sop a ohte nk adams 4 3 13 Numeric Precision 2m ue RE RePEc ee e idees 5 3 1 4 Boolean Expressions er ic pep ted cae deta pr UN IECUR RHET TC ERU UE 5 SAD AIA So oie oh REPE
59. P 1 NS 1 NFS 0027 BY FAST 1 NFS NS NFP DELTA 0028 IF NFS gt 0 Replace failed processor with failed spare 0029 RANTO NP NFP NS 1 NFS 1 0030 BY FAST NFS NS NFP DELTA 0031 ENDIF PARSING TIME 0 21 sec RULE GENERATIO IME 0 02 sec NUMBER OF STATES IN MODEL 13 NUMBER OF TRANSITIONS IN MODEL 24 6 DEATH STATES AGGREGATED INTO STATE 1 N PROCS 3 N SPARES 2 LAMBDA P 1 LAMBDA 1 DELTA 3 6E The model file generated by ASSIST for this example is w Dd Ed U A 36 Figure 9 Semi Markov triad model with cold spares ASSIST state numbers 37 Figure 10 Semi Markov triad model with cold spares SURE state numbers 38 2 3 0 2 0 3 3 1 2 0 3 0 LAMBDA P 2 3 0 2 0 4 3 0 2 1 2 LAMBDA S 3 3 1 2 0 5 3 0 1 0 FAST 1 0 2 1 DELTA 3 3 1 2 0 1 3 2 2 0 DEATH 3 1 LAMBDA P 3 3 1 2 0 6 3 1 2 1 2 LAMBDA 8 4 3 0 2 1 6 3 1 2 1 3 0 LAMBDA P 4 3 0 2 1 7 3 0 2 2 2 LAMBDA S 5 3 0 1 0 8 3 1 1 0 3 0 LAMBDA P 5 3 0 1 0 9 3 0 1 1 1 LAMBDA_S 6 3 1 2 1 9 3 0 1 1 FAST 1 1 2 1 DELTA 6 3 1 2 1 8 3 1 1 0 FAST 1 2 1 DELTA 6 3 1 2 1 1 3 2 2 1 DEATH 3 1 LAMBDA_P
60. R IS INACTIVE id BUILT IN FUNCTION func gt This error indicates that an identifier was referenced but its use is no longer valid It usually occurs when a FOR index is referenced after the matching ENDFOR but the error can also occur if an identifier name is referenced without redefinition after it has already been used in the parameter list for the definition of a prior FUNCTION or IMPLICIT The identifier in error was passed to the named built in function SCOPE OF IDENTIFIER IS STILL ACTIVE gt This error indicates that the user tried to redefine an identifier when it was still being used for another purpose This error usually means that two nested FOR constructs are using the same index variable name The user should change the name of one index variable 82 Pl SCRATCH EXPRESSION STORAGE OVERFLOW SPECIFY E OPTION COMMAND LINI OPTIONS TOO BIG gt This error indicates that the user asked for more memory for the expression storage than allowed Try asking for less The default is e 100 for workstations and e 50 for the IBM PC SCRATCH EXPRESSION STORAGE OVERFLOW SPECIFY E OPTION id gt This error indicates that the ASSIST program cannot hold all the expressions it needs at once It usually indicates use of very many state space variables at a single level in the SPACE statement or it can indicate use of very many expressions in the rules nested betw
61. RI Reset Rew See beens OES ee eae eel ep LS heres 6 3 1 6 Ranges ice uis Naren Said Biel Aon Se bier eU Aad Seaplane 6 3 T E Repetitioris z o oientsenedieeSeb tence toe eae S bad neca duce we t E Erat e SP Receta as 7 3 1 8 Builtsim Butictiohls ate ie tee ete ex wr d eg ees n ETE Sly 7 3 1 8 1 Mathematical functions in eiee inato a a eee E E s 7 3 1 8 2 Trigonometric functions rnes ne e a a E ran 7 3 1 8 3 Combinatorial functions nos cccr eere secan sea a eee ee eee s 8 3 1 8 4 Array list functions ieie cnet Aee e a i ie 8 3 2 Language Statements 22 eed eee eee ADS Rae ARR UE eae RII a Ags SOR S S 9 3 2 l Setup Section nk Seda r IDA RU IR eE h a eo ee oS Ee Sees ober 10 3 2 1 1 Constant definition statement 0 00 000 es 10 3 2 1 2 Option definitions ae hace hon as de dun ads snes wn diana Ge ee we a 11 3 2 1 3 INPU T statement 2 ek deter e cated gabe ba ue Cotes 12 3 2 1 4 COMMENTS 232 eec S etr Borse e tado stu Eo vides Er Vado rr eda 13 3 2 1 5 Quoted SURE statement enr nen iE LEA Rer Are din a Ba gina Ragen 13 3 21 6 SPACE statements deae ub RR URS em GE E 14 3 2 2 Start SeCUODo ez iu heo UE RP Be PReRPDePpeeviddeeene euer nS 16 3 2 3 IMPLICIT Statement 1 5 ter oe Bl rate Lee e Es 16 3 2 4 FUNCTION Statement i Secs cede ue melo mw Mere Rer DR Era Wen e 17 3 2 5 VARIABLE Statement eee s 18 3 2 0 START Statemeht e eR DER CERE PIS ENIM Ere REPE 20 3 2 J Rule Sectols uer
62. SE CONTACT COMPILER SUPPORT Not defined for SSV s FUNCTION s INTERNAL s save value in number table gt This error indicates a problem so serious that ASSIST could not deal with it Try fixing all other errors first I INTERNAL ERROR PLE ASE Y F state spac XC ds limit CONTACT COMPILER SUPPORT Number of bits 8200 num in This error indicates a problem so serious that ASSIST could not deal with it Try fixing all other errors first When the error message says Number of bits in state space exceeds limit try sim plifying the model by using fewer state space variables INTERNAL ERROR PLEASE CONTACT COMPILER SUPPORT id gt This error indicates a problem so serious that ASSIST could not deal with it Try fixing all other errors first INVALID COMMAND LINE OPTION opt gt This error indicates that the user specified an unrecognizable command line option The name of the option was probably misspelled Check the spelling against that listed for the desired option in appendix E I INVALID COMMAND LINE OPTION opt gt This error is the VMS equivalent of the previous error 74 INVALID NUMERIC VALUE id gt This error indicates that a value was specified that is not in the range of valid values for the state ment or construct in question For example in an option definition statement only the values 0 1 and 2 are
63. SSIST could not deal with it Try fixing all other errors first INTERNAL ERROR PLEASE CONTACT COMPILER SUPPORT BAD TERNARY OP gt This error indicates a problem so serious that ASSIST could not deal with it Try fixing all other errors first INTERNAL ERROR PLEASE CONTACT COMPILER SUPPORT BAD UNARY OP gt This error indicates a problem so serious that ASSIST could not deal with it Try fixing all other errors first INTERNAL ERROR PLEASE LENGTH BUILT IN OP gt This error indicates a problem so serious that ASSIST could not deal with it Try fixing all other errors first CONTACT COMPILER SUPPORT BAD VARIABLE ARGUMENT INTERNAL ERROR PLEASE CONTACT COMPILER SUPPORT BUFFER OVERFLOW WHEN PARSING SPACE PICTURE TRY USING 200 OR FEWER STATE SPACE VARIABLES PER NESTING LEVEL gt This error indicates a problem so serious that ASSIST could not deal with it Try fixing all other errors first INTERNAL ERROR PLEASE CONTACT COMPILER SUPPORT Expression evaluation stack overflow Try simplifying expression via use of named constants or rebuild ASSIST with a larger value for EVAL_STACK_DIM expression on line num gt This error indicates a problem so serious that ASSIST could not deal with it Try fixing all other errors first INTERNAL ERROR PLEA
64. SSIST input language Cer tain conventions will be used throughout this manual for introducing the syntax of the ASSIST input language statements 1 All reserved words will appear in bold as in FOR and IN 1 10 2 Items that are enclosed in angle brackets such as lt expression gt are expressions that must be supplied by the user 3 Large braces such as and are used to denote constructs that may be omitted or repeated as many times as desired 4 Large brackets such as and are used to denote optional constructs that may be present once or omitted 5 The suffix list denotes a sequence of at least one construct in which each construct is separated by a delimiter such as a comma The ASSIST input file can be subdivided into three parts The setup section is first in the input file it contains definitions and terminates with the SPACE statement The start section of the file contains more definitions and a single START statement it can also contain FUNCTION and IMPLICIT definitions The rule section of the file begins with the first model generation rule statement such as a TRANTO or DEATHIF statement The rule section of the file must not contain any definitions 9 Definitions can be organized in any sequence within the setup and start sections The only restric tion is that an identifier must be defined before it is referenced Comments may be placed anywhere in the ASSIST inp
65. T NWS warm NFS warm lt NSI warm IF NWS warm gt 0 Arrival of permanent warm spare fault TRANTO NWS warm NFS warmt BY NWS warm LAM warm ck ock ck ck ck ck ck ck ck ck ck ck ck ck ck ck ck Pk Mk kA A x Mk ko ko KKK kk ck CkCckckck ck ckckckckckckokckckck ck ckckckck ck kck ck ck ck kk KK K kk SPARE POOL cold KK K kk kk ck Ck Cckckckckckckckckckckockckckck ck ckckckckck ck ck ck ck ck kk KKK KKK KKK KEK KKK KKK KKK KKK ck ck ck ck ck ck kk ASSERT NS cold lt NSI_cold KKK KKK KKK KEK KKK KKK KKK KKK ck ck ck ck ck ck KK KKK KK KKK KKK KKK KKK KKK KKK KKK ck ck ck KK KKK KKK MISC DEATH amp PRUNE KK K KKK KKK KKK KKK KEK KKK KKK KKK KKK KKK ck ck ck KK KKK KKK KKK KEK KKK KKK KKK KKK KKK ck ck ck KK DEATHIF TFA_triad gt TWA_triad 17 Command Line Parameters and Options This section details the command for executing the ASSIST program The program is written in the C programming language and will execute on a VAX under the VMS operating system or on a Sun 3 or Sun SPARCstation under the UNIX operating system An ANSI standard C compiler is required to compile the program The current Sun C compiler will not compile ASSIST but Sun is planning to release an ANSI C compiler in the future However an ANSI C compiler for the Sun computers gcc is available from the Free Software Foundation
66. The C compiler available with the VAX VMS operating system is an ANSI C compiler When running the ASSIST program the only positional parameter is the name of the input file being processed The ast suffix may be omitted from the file name on the ASSIST command line Options are also allowed The file name may not follow an option but must precede all options Options must be preceded by a slash under VMS as in map and must be preceded by a dash under UNIX as in map Options may be specified either in upper or lower case The normal UNIX case sensitivity is not enforced on the ASSIST command line options The syntax is assist or assist filename or assist lt option list gt or assist lt filename gt lt option list gt 2SPARCstation a trademark of SPARC International 50 Respective examples are assist or assist foo or assist xref or assist foo xref If the file name is omitted ASSIST will prompt for one There are several options that may be listed in any order on the command line These options are all enumerated in appendix E A few important options are discussed below 17 1 Controlling Error Warning Limits The lel option controls the maximum number of errors allowed on a single ASSIST input line The el option controls the maximum cumulative number of errors allowed throughout the whole input file The lwl option controls the maximum number of warnings allowed on a single ASSIST
67. The failure rate of each active processor is p The failure rate of a cold spare processor is A e A failed active processor is replaced by a spare processor at fast exponential rate 6 The third transition type requires a more complicated TRANTO statement because the spare proces sor may or may not have failed before reconfiguration The DEATHIF statement describes the death condition for the model e System failure occurs unless a majority of the active processors are nonfaulty By changing the value of N_SPARES a similar system with a different number of initial spares may be modeled The following dialog consisting of an execution of ASSIST followed by an execution of SURE will process the input file 9 assist triadcold ASSIST VERSION 7 1 NASA Langley Research Center PARSING TIME 0 18 sec generating SURE model file RULE GENERATIO IME 0 02 sec NUMBER OF STATES IN MODEL 13 NUMBER OF TRANSITIONS IN MODEL 24 6 DEATH STATES AGGREGATED INTO STATE 1 SURE V7 9 8 NASA Langley Research Center 1 readO triadcolg 0 03 SECS TO READ MODEL FILE 37 run MODEL FILE triadcold mod SURE V7 9 8 14 Sep 93 17 11 45 35 triadcold ast LOWERBOUND UPPERBOUND COMMENTS RUN 1 1 66645e 10 1 69427e 10 prune 1 2e 19 gt 25 PATH S TO DEATH STATES 2 PATH S PRUNED
68. XPRESSION CONSIDER THE USE OF A FUNCTION OR IMPLICIT id This error indicates that a variable was referenced in a constant expression It can occur in a con stant definition statement an INPUT statement or in a START statement Many input files built for older versions of ASSIST will get this error message because the old variable definition state ment was replaced with the new IMPLICIT definition statement See section 3 2 3 for details on the IMPLICIT statement VARIABLES NOT ALLOWED IN FUNCTION DEFINITION BODY ONLY NAMED CONSTANTS MAY BE INHERITED gt This error indicates that the user tried to reference a variable from a function body If the variable is a state space variable try using an IMPLICIT function definition instead If the variable is a parameter from a previous FUNCTION or IMPLICIT it was probably omitted from the parame ter list for the new function WILD SUBSCRIPT NOT ALLOWED EXCEPT IN CONTEXT OF APPLICABLE BUILT IN FUNC TION id This error indicates that an array was referenced with an asterisk instead of an array subscript in the wrong context If the user meant to compute the subscript as the product of two quantities an identifier or literal value must precede the asterisk If the user meant for a wild subscript to be present a function such as SUM or COUNT is probably missing C 2 List
69. Y J LAMBDA 25 ENDFOR DEATHIF NC I NF I ENDFOR Each ENDFOR matches the most recently preceding FOR The FOR constructs in the example above generate 10 5 x 2 TRANTO rules one for each pair of LJ values 1 1 1 2 2 1 2 2 5 2 Five DEATHIF rules are also defined by using values of I from 1 to 5 The body of the FOR may con tain any valid rules including block IF s and nested FOR s 12 2 7 4 ASSERT statement The ASSERT statement is used to specify a condition that should be true for every model state During model generation each model state is checked for compliance with every ASSERT condition If any ASSERT conditions are violated the ASSIST program will print a warning to both the terminal and the log file ASSERT statements are useful for checking that the sys tem described in the ASSIST input file has the intended properties The syntax is ASSERT condition The ASSERT condition is a Boolean expression with optional parentheses For example ASSERT NWP NFP NP Check that working processors failed processors always equal total 4 processors ASSERT NP 0 ASSERT NP 5 NWP 4 ASSERT NP gt 0O AND NWP 20 AND NFP lt 100 ASSERT NP 0 AND NWP gt 0 AND NOT NFP gt 100 12 2 7 5 DEATHIF statement The DEATHIF statement specifies which states are death states i e absorbing states in the model The
70. a parameter to the SIZE function when the syntax for ASSIST required an array The token found instead of the array is echoed 67 CALLING PARAMETERS NOT ALLOWED ON IMPLICIT REFERENCES id gt This error indicates that an IMPLICIT function which was declared without a parameter list was referenced with a passed parameter list CANNOT MIX REAL NUMBERS INTO INTEGER ARRAY CONSTANT gt This error indicates that the user was in the process of defining a constant integer array when a real number was encountered The ASSIST file determines the type of array from the presence or absence of a period in the first element of the array If the array is a real array with some integer values then the first element in the array must have a decimal point For example FOO 7 0 11 8 5 The decimal can be omitted for any integer elements in the real array unless the integer element comes first If the array is an integer array then no decimal points are allowed in any of the elements CANNOT OPEN FILE PLEASE CONTACT SYSTEM MANAGER foo ast gt This error indicates that there is probably something wrong with the disk drive since ASSIST could not open the input file The system manager might have the disk drive dismounted or other wise unavailable ASSIST will usually tell the user why it cannot open a file If it does not the sys tem manager would be aware of any unusual circumstances
71. ables Consider the following example SPACE AMAT ARRAY 1 3 1 3 OF 0 7 BMAT ARRAY 1 3 1 3 OF 0 7 NCF 0 7 Number of component failures for prune Hy I IMPLICIT CMAT AMAT BMAT I J K AMAT I J BMAT J K 12 2 4 FUNCTION Statement The FUNCTION statement is used to define a new function A function computes a value based upon constants and parameters passed to the function The syntax of a function definition follows FUNCTION lt identifier gt parameter list lt body gt The lt parameter list gt is made up of zero or more identifiers separated by commas All parameters are positional and must therefore be passed in a consistent order The user decides how many parameters a certain function will have The user may not vary the number of parameters that are passed from the 17 number of parameters that are defined The parameter names in the parameter list are separated by com mas Parameter names may be reused in other IMPLICIT or FUNCTION definitions or as FOR indi ces but they cannot be named constants or state space variable names The lt body gt of the FUNCTION definition is the expression that defines the value as a function of the parameters The FUNCTION may be invoked in TRANTO DEATHIF PRUNEIF ASSERT IF or FOR state ments or in later IMPLICIT or FUNCTION definitions by giving its name followed by the values for each of its parameter
72. acters because ASSIST automatically generates scalar identifier names to pass to SURE by appending the index value If the upper bound of a singly subscripted constant array index is no more than 9 then 10 characters can be used for the array name If the upper bounds of the two doubly sub scripted constant array indices exceed 9 then 6 or fewer characters may be required To illustrate this consider the arrays SINGLI DOUBLI 1 2 4 4 0 00333 Los 2 l The resulting model file output will contain the lines Lya Meaty d 1 22 249 SINGLE 1 1 2 SINGLE 2 4 4 SINGLE 3 0 00333 DOUBLE 1 1 1 1 DOUBLE 1 2 1 2 DOUBLE 1 3 1 3 DOUBLE 2 1 2 1 DOUBLE 2 2 2 2 DOUBLE 2 3 2 3 All these model file identifiers are unique to their first 12 characters An error message will be printed by ASSIST if two separate constant identifier names are not unique to the first 12 characters 12 2 1 2 Option definitions The ASSIST language has some predefined identifiers called options that can have states set to one of three values The values are on off or full equivalently they are inte ger values of zero one or two The syntax of an option definition is option name flag status where the flag status is one of the following OFF or ON FULL or 11 The following options are currently defined in the ASSIST language The COMMENT option is used to control w
73. ain options such as pipe are valid only on UNIX systems They will not work on VMS This serious warning message appears when 1 or more levels of error reporting are requested PROGRAM DOES NOT CONTAIN ANY DEATHIF STATEMENTS token gt This warning indicates that the program did not contain any DEATHIF statements This warning message appears when 2 or more levels of error reporting are requested TESTS FOR EQUALITY INEQUALITY OF REALS CAN PRODUCE INCORRECT RESULTS gt This warning indicates that the user tried to test for one real equal to or not equal to another real The user should use relations such as lt or gt instead of and lt gt This minor warning message appears when three or more levels of error reporting are requested THE C OPTION STATEMENT SHOULD APPEAR BEFORE ANY OTHER STATEMENTS IN THI INPUT FILE foken This warning indicates that a C OPTION statement appeared out of sequence In most instances this will cause serious problems In some instances this may be acceptable For exam ple it is okay to change the maximum number of errors line at various places in the input file but increasing memory allocation limits must be done first This option can be used as the last line of the input file to change the warning error limits for the rule generation phase This serious warning message appears when one or more levels
74. al Expressions Precedence Category Operator Associativity Operand type Result Highest Indexing Left to right Anyl int Same Grouping Left to right Any Same Binary Right to left Real int Real Unary Right to left Realint Same Unary NOT Right to left Boolean Boolean Binary vt Right to left Real int Real int Binary DIV MOD CYC Left to right Real int Same real int Binary Left to right Real int Same Binary lt gt lt gt lt gt Left to right Real int Boolean Binary Left to right Boolean Boolean Binary AND amp Left to right Boolean Boolean Lowest Binary OR XOR Left to right Boolean Boolean N A Rate dest N A State space var Same A list of sample expressions follows Each expression is followed by an arrow and a description of the ASSIST interpretation of the expression The dash is used for both unary negation and binary subtraction 5 6 8 5 6 8 5 6 8 5 6 8 The following are legal P AND Q OR P AND R P OR Q AND P OR R P AND Q OR P AND R P OR Q AND P OR R NP MOD NFP I NP MOD NFP I I NP MOD NFP I NP MOD NEP I NP DIV NFP I NP DIV NEP PSI 2 0 MU PSI 2 0 MU PSI MU OMEGA PSI MU OMEGA PSI MU OMEGA PSI MU OMEGA PSI MU OMEGA PSI MU OMEGA PSI EPS PSI EPS PSI MU 3 PSI
75. al types of statements are valid in the rule section These are described below 12 2 7 1 TRANTO statement The TRANTO statement is the heart of the model generation process and is used to describe the state transitions in the model The model is generated by recursively applying the TRANTO rules to each model state beginning with the START state The transitions represent the elapsed time between system states which are stochastic processes defined by probability distributions In the restricted class of Markov models all transitions are expo nentially distributed and are completely defined by a simple rate parameter In the more general semi Markov model any distribution can be used to describe the elapsed time Transitions between model states are specified using TRANTO statements Typical TRANTO statements have three main parts or clauses 667 1 An optional IF conditional expression also called the IF clause 2 A required destination expression also called the TRANTO clause or the destination clause 3 A required rate expression also called the BY clause or rate clause The optional first clause contains a Boolean expression that describes the states for which the transi tion is valid in terms of their state space variable values The second clause defines the destination state for the transition in terms of state space variable values The third clause defines the distribution of elapsed time fo
76. allowed corresponding to OFF ON and FULL respectively PI INVALID PROMOTION OF lt boolean gt TO lt integer gt gt This error indicates that the user tried to mix Boolean and integer values in the same expression The built in function COUNT can be used to convert a Boolean to an integer and the relational operators can be used to convert a number to a Boolean For example 6 COUNT FLAG or I lt gt 0 respectively INVALID PROMOTION OF boolean TO real gt This error indicates that the user tried to mix Boolean and real values in the same expression The built in function COUNT can be used to convert a Boolean to an integer and the relational operators can be used to convert a number to a Boolean For example 6 COUNT FLAG or I lt gt 0 respectively INVALID PROMOTION OF integer TO boolean gt This error indicates that the user tried to mix Boolean and integer values in the same expression The built in function COUNT can be used to convert a Boolean to an integer and the relational operators can be used to convert a number to a Boolean For example 6 COUNT FLAG or I lt gt 0 respectively INVALID PROMOTION OF real TO boolean gt This error indicates that the user tried to mix Boolean and real values in the same expression The built in function COUNT can be used to convert a Boolean to an integer and the relational operat
77. and clauses and nested IF s that were allowed in the past This feature gives the user a lot more flexibility when describing system behavior The syntax of a block IF is IF condition THEN lt more rules gt ELSE lt more rules gt ENDIF Even though a block IF can be typed on a single line as in the example IF NWP gt 0 THEN TRANTO NWP NCF BY NWP LAMBDA DEATHIF ENDIF it is generally clearer to use multiple lines and indentation as in IF NWP 0 THEN TRANTO NWP NCF BY NWP LAMBDA DEATHIF NDIF Eri A semicolon is not necessary after the word THEN in the IF clause If present it will be ignored since the empty statement is also a valid ASSIST statement Do not think of the block IF in the procedural sense Think of it as conditionally selecting a set of rules Block IF constructs can be nested with other constructs For example IF NFP 0 THEN FOR III IN 1 3 ASSERT NOT W III AND F III either working or failed but not both IF NOT W III THEN TRANTO W III TRUE BY FAST PROB DELTA1 disappearance TRANTO W III TRUE NS BY FAST 1 0 PROB DELTA2 reconfiguration ENDIF ENDFOR ENDIF 12 2 7 3 FOR construct Often several rules are needed that are identical except that they operate on different state space variables The different state space var
78. at a single level in the SPACE state ment than anticipated by ASSIST The user should try to limit the number of state space variables as much as is feasible Unpruned models with a huge state space will seem like they run forever The limit can be raised The default is pic 100 for workstations and pic 100 for the IBM PC SPACE STATEMENT OVERFLOW SPECIFY PIC OPTION id This error is the VMS equivalent of the previous error SPECIAL VMS ERROR NUMBER errornumber This error indicates that an error specific to the VMS operating system was encountered START STATEMENT IS MISSING gt This error indicates that the first rule was encountered yet the required START statement was absent STATE SPACE CANNOT BE EMPTY AT LEAST ONE STATE SPACE VARIABLE REQUIRED id gt This error indicates that a SPACE statement was declared without any state space variables See section 3 2 1 6 for the correct syntax for the SPACE statement 83 STATE SPACE VARIABLE DOES NOT HAVE A VALUE UNTIL AFTER PARSING IS COM PLETE AND RULE GENERATION HAS STARTED gt This error indicates that a state space variable was referenced in a context where a constant was required It can occur in a constant definition statement an INPUT statement or in a START statement STATE SPACE
79. ates that did not satisfy the first DEATHIF but satisfied the second and so on Thus the probability of system failure caused by each condition specified by a DEATHIF statement will be given by the probability of reaching the corresponding death state Use of ONEDEATH FULL is equivalent to ONEDEATH ON The TRI M option controls the kind of trimming that is done in the model Trimming is discussed in section 4 2 The default is TRIM OFF Unlike constant definitions which are written to the model file option definitions are known only to ASSIST 12 2 1 3 INPUT statement An INPUT statement specifies that the user should be queried for the values of one or more named constants The syntax is INPUT lt input list gt where lt input list gt consists of a series of identifiers separated by commas and where each identifier is optionally preceded by a prompt message For example interactive input for identifiers LAMBDA and DELTA may be specified as follows INPUT LAMBDA DELTA This statement will result in the default prompt messages during execution LAMBDA DELTA For the above example the user is first prompted for LAMBDA and must enter an integer real value or expression The user is then prompted for DELTA and must again enter an integer value real value or expression Each expression must be entered with a terminating se
80. ay NF of range 1 to 3 could represent the number of each type of compo nent that is faulty and active The death condition could be described by the following FOR I IN 1 3 DEATHIF 2 NF I gt NA I ENDFOR Thus in all states of the Markov model where 2 times the value of NF for one of the three compo nents is greater than or equal to N for the same component system failure occurs Even though a FOR can be typed in all cases on a single line as in the example FOR I IN 1 3 DEATHIF 2 NF I gt NA I ENDFOR it is generally clearer to use indentation as in FOR I IN 1 3 DEATHIF 2 NF I gt NA I ENDFOR A semicolon is not necessary after the set in the IN clause If present it will be ignored since the empty statement is also an ASSIST statement The FOR variable index may be referenced only by statements between the FOR clause and its matching ENDFOR The same variable name can be used for FOR constructs that follow each other in series however a unique variable name must be used for a FOR index that is nested inside another FOR The rules between the set and the ENDFOR also called the body of the FOR are processed with the index varying over all specified values in the set FOR constructs may be nested as in the following SPACE NC ARRAY 1 5 OF 0 6 NF ARRAY 1 5 OF 0 3 FOR I IN 1 5 FOR J IN 1 2 IF NC I gt J TRANTO NF I NF I 1 B
81. between the upper and lower bound on the range of values cannot exceed 255 NUMERIC ITEM EXPECTED id BUILT IN FUNCTION func This error indicates that something other than a numeric item was encountered in the parameter list for a built in function such as SUM when the syntax for ASSIST requires a numeric item The token found instead of the numeric item is echoed ONLY ONE WILD SUBSCRIPT ALLOWED PER ARRAY REFERENCE id gt This error indicates that a doubly wildcarded subarray was passed to a list function as in SUM FOO The syntax allows only for operation on a single row or a single column If the whole table must be summed in both directions then the correct syntax is SUM FOO ONLY READ PERMISSION CAN BE GRANTED foo ast gt This error indicates that the user does not have write permission to the directory in which the input file resides The user should copy the input file to his own directory and run ASSIST there If that does not work contact the local system manager for help ONLY STATE SPACE VARIABLES MAY BE LISTED IN THE STATE SPACE VARIABLI LIST id This error indicates that the user attempted to list something other than a state space variable name between the square brackets in an IMPLICIT definition statement If the identifier is a named constant it can be used without being listed If the ide
82. ble list for TOTALF even 19 though it is only referenced indirectly When NFP is referenced in the IF clause the value of III is passed as a subscript to the array NFP 12 2 6 START Statement The START statement is used to specify the initial state of the system being modeled i e the prob ability that the system is in this state at time 0 is 1 The state is defined by an n dimension vector of inte gers or Booleans Each ASSIST input file must contain exactly one START statement that corresponds precisely to the SPACE statement in its setup section i e the START statement must include the same number and type integer versus Boolean values in the same sequence as specified in the SPACE statement and they must use identical nesting To make variable sized arrays more usable repetition may be used in the START statement as in the following example INPUT NX SPACE NP ARRAY 1 2 NF NC ARRAY 1 NX OF BOOLEAN START 2 OF 6 0 NX OF FALSE This START statement fills array NP with 6 s sets NF to 0 and fills array NC with FALSI GI n The START statement syntax is START lt space expression gt The syntax of a lt space expression gt is lt space expr item gt lt Space expr item gt The syntax of a lt space expr item gt is expr OF lt expr gt or lt space expression gt Like the SPACE statement the START statement syntax is recursive becau
83. cates that the user used a reserved word in the wrong place LEFT EXPECTED token gt This error indicates that something other than a left parenthesis was encountered when the syntax for ASSIST requires a left parenthesis The token found instead of the left parenthesis is echoed LEFT EXPECTED NO MATCHING LEFT FOR THIS gt gt This error indicates that something other than a left angle bracket was encountered in a rate expression when the syntax for ASSIST requires a left angle bracket The token found instead of the left angle bracket is echoed LEFT EXPECTED token gt This error indicates that something other than a left bracket was encountered in a rate expression when the syntax for ASSIST requires a left bracket The token found instead of the left bracket is echoed LOWER BOUND TO LEFT OF RANGE MUST BE UPPER BOUND TO RIGHT min max gt This error indicates that a backwards range was specified in a SPACE statement either as an array subscript range or a state space variable value range The user must specify the minimum value of the range before the maximum value for the range For example say 6 10 and not 10 6 MISSING TOKEN INSERTED BY PARSER gt This error indicates that something other than a closing parenthesis was encountered when the syn tax for ASSIST requires a closing parenthesis Th
84. ce The variable can be either a scalar or an array Vari ables can be used to make an ASSIST description more understandable without incurring the additional memory required to store extra state space variable values For example if NWP is a state space variable representing the number of working processors and NI is a constant denoting the number of initial processors the declaration VARIABLE NFP NWP NI NWP defines NFP denoting the number of failed processors to be the difference between the initial number and the current number of working processors The above variable can be referenced as illustrated in the following DEATHIF statement DEATHIF NWP lt NFP VARIABLES and IMPLICITS often produce the same results The main difference between VARIABLES and IMPLICITS depends upon when the expression evaluation is performed With an IMPLICIT the expression to the right of the equals sign is not evaluated until it is actually used With a VARIABLE the expression is evaluated once for each new state regardless of whether or not the VARIABLE statement is ever referenced If the expression is going to be referenced inside a loop or used many different times a VARIABLE will probably be more efficient than an IMPLICIT If 18 however the references to the expression are all protected by IF tests that hold true
85. cifies how deeply a space statement can be recursively nested The default is 16 on most systems 8 on the IBM PC rule nnn Specifies the maximum number of rules that can be nested inside a single block IF or FOR construct The default is 4096 for most systems 1024 on the IBM PC pic nnn Specifies the maximum number of nodes that can be on the stack when parsing a state space picture The number of state space variables may exceed this number only if the state space picture is recursively defined The default is 100 lel nnn Specifies the line error limit If the number of errors per line ever exceeds this value then ASSIST will quit processing the input file immediately after printing one additional and appropriate error message The default is a maximum of five errors allowed per line lwl nnn Specifies the line warning limit If the number of warnings per line ever exceeds this value then ASSIST will quit processing the input file immediately after printing an appropri ate error message The default is a maximum of five warnings allowed per line el nnn Specifies the error limit If the cumulative errors ever exceed this value then ASSIST will quit processing the input file immediately after printing one additional and appropri ate error message The default is a maximum of 40 errors allowed per input file wl nnn Specifies the warning limit If the cumulative number of warnings
86. ction than it is defined to handle LH 81 RIGHT EXPECTED func REQUIRES EXACTLY num PARAMETERS AND NO MORE gt This error indicates that something other than a right parenthesis was encountered in the parameter list for a built in function when the syntax for ASSIST requires a right parenthesis The token found instead of the right parenthesis is echoed This error usually occurs when more parameters are passed to a built in function than it is defined to handle GI RIGHT EXPECTED id gt This error indicates that something other than a right parenthesis was encountered when the syntax for ASSIST requires a right parenthesis The token found instead of the right parenthesis is echoed RIGHT EXPECTED id This error indicates that something other than a right angle bracket was encountered when the syn tax for ASSIST requires a right angle bracket The token found instead of the right angle bracket is echoed This usually indicates that the user is missing a right angle bracket when White s Method is used to specify the transition rate expression in a TRANTO statement RIGHT EXPECTED id gt This error indicates that something other than a right bracket was encountered when the syntax for ASSIST requires a right bracket The token found instead of the right bracket is echoed RULE SCRATCH STORAGE OVERF
87. d NFP number of failed pro cessors and can take on values between 0 and 3 The third statement indicates that the model starts in state 3 0 This state has three processors and none failed The words LAMBDA NP and NFP are simply names chosen for this particular example they have no intrinsic meaning to the ASSIST program The DEATHIF statement indicates that system failure death occurs when the number of failed processors equals or exceeds the number of working processors The last statement is a TRANTO statement The IF clause specifies that this transition is valid if there is still a working processor left The TRANTO clause describes how to compute the ordered pair representing the new state from the old state values In this example the number of faulty processors is increased by one The BY clause defines the rate at which the transition occurs Every ASSIST input description must contain a SPACE statement a START statement at least one TRANTO statement and at least one DEATHIF statement Figure 7 shows the semi Markov example model for the system with the states labeled with the corresponding ASSIST state space values eo 0 2 Figure 7 Semi Markov triad model ASSIST state numbers 12 Input Language Syntax This section contains a detailed description of the ASSIST input language syntax The first sub section introduces the lexical details and basic building blocks of the language suc
88. d begins oper ation in state 1 with three working processors Processor failures are exponentially distributed at a rate of Since there are three processors that can fail there is a transition leaving state 1 at a rate of 3A After one of the three processors fails the system is in state 2 In this state the system is still functional since there are two working processors and one failed one The failed processor is outvoted by the good processors After one of the two remaining processors fails at rate the system is in state 3 This state is a failure death state because there are two failed processors and one good processor and the majority voter can no longer correctly eliminate the erroneous outputs Death states absorbing states are pre cisely those with no arrows leaving them Figure 6 Semi Markov triad model SURE state numbers An ASSIST input description that would generate the above model is LAMBDA 1 2E 4 SPACE NP 1 3 NFP 0 3 START 3 0 DEATHIF NFP NP NFP IF NFP 3 TRANTO NFP NFP 1 BY NP NFP LAMBDA 2 The first input description statement defines LAMBDA a constant with a value of 1 2 x 107 This constant will be used to denote the exponential processor failure rate in the example The next statement defines the state space as an ordered pair of integers The first integer is named NP number of proces sors and can take on values between 1 and 3 The second integer is name
89. e ready list increment pointer to next ready state ENDFOR print extra trim transitions IF trimming is on THEN FOR current state I trim state only DO print transition from current state to trim death state BY TRIMOMEGA ENDFOR IF pruning with TRIMOMEGA i e trim 2 THEN FOR current state IN prune states DO print transition from current state to current prune death state BY TRIMOMEGA ENDFOR ENDIF ENDIF FOR all TRANTO s DO F never referenced THEN print a warning message that TRANTO was never used ENDIF ENDFOR IF fatal error occurred THEN flag model file as erroneous ENDIF STOP 15 File Processing The ASSIST program reads an input file containing the model definition rules and creates several output files The two most important output files are the model file and the log listing file The diagram in figure 8 illustrates the data information flow between files during the processing of an ASSIST input file These files are described in sections 6 1 through 6 1 4 31 ASSIST Parse phase CN Model generation phase foo aobj Figure 8 Data file flow in ASSIST 15 1 Input File The input file contains a sequence of ASSIST instructions and the user must create the file by using a text editor or a tool such as TOTAL By convention the input file
90. e model To be conservative lt trimomega gt must be greater than or equal to the sum of the failure rates for all components still in the system when any pruned state is reached 13 3 Assignment of State Numbers State numbers are assigned according to the following hierarchy 1 When ONEDEATH is ON death state numbers are always assigned first 2 The pruned death states are assigned next 3 If TRIM is ON or FULL 2 1 the TRIM death state is assigned next 4 If TRIMis FULL 2 the individual pruned states are assigned next 5 If TRIM is ON or FULL 2 1 the trim state is assigned next 6 The start state is assigned next 14 Model Generation Algorithm The model generation algorithm builds the model from the start state by recursively applying the TRANTO rules A list of states to be processed called the ready set begins with only the start state Before application of a rule ASSIST checks all the ASSERT conditions and prints any warning mes sages All death conditions are then checked to determine if the current state is a death state Since a death state denotes system failure no transitions can leave a death state If the state is not a death state ASSIST then checks all pruned conditions to determine if the current state is a pruned state If ASSIST finds a state space variable that is out of range or if ASSIST detects some other error in the state the state is treated as a death state
91. e model to be generated As flight critical systems become more complex and more highly integrated the Markov models describing them will become enormously complex However our experience has been that even the most complex system characteristics can usually be described by relatively simple rules The models only become complex because these few rules combine many times to form models with large numbers of states and transitions between them Furthermore the process of describing a system in terms of the model generation rules forces the reliability engineer to clearly understand the fault tolerance strategies of the system and the abstract description is also useful for communicating and validating the system model Further levels of abstraction are both possible and feasible Several research prototype computer programs to generate ASSIST input descriptions from even more abstract system descriptions have been developed including the Table Oriented Translator to the ASSIST Language TOTAL ref 8 and the Reliability Estimation Testbed REST ref 9 NASA Langley Research Center Hampton VA 23681 0001 April 7 1995 53 Appendix A Expression Precedence This appendix defines the order of precedence used by ASSIST in evaluating mathematical expres sions The operator precedence is shown in the following table which is sorted from highest precedence to lowest precedence Table A1 Order of Precedence Used by ASSIST for Mathematic
92. e scrambled with the standard error messages from ASSIST The nostats option will not suppress error and warning messages If the VMS or other non UNIX user attempts to use the pipe option a warning message will be printed WARNING OPTION ONLY VALID ON A UNIX SYSTEM OPTION IGNORED pipe 17 5 Batch Mode The bat option causes ASSIST to run in batch mode In batch mode the ASSIST command line is echoed to standard error A batch process will usually redirect standard error to a file instead of to the user s monitor screen If the batch process invokes ASSIST many times and one of the input files hap pens to contain some errors the user will be able to tell which file was being processed by examining the echoed command line 17 6 Controlling Printing of Warning Messages The w option specifies the number of warning levels that are printed The lower the number of warning levels reported the fewer warning messages there are 18 Concluding Remarks The ASSIST program automatically generates a semi Markov reliability model from an abstract input language Semi Markov models have the flexibility to accurately represent virtually any fault tolerant system The ASSIST input language provides an abstraction for describing rules rather than 52 individual transitions However the flexibility of semi Markov modeling is maintained because no assumptions are made about the system the rules themselves completely specify th
93. e token found instead of the closing parenthesis is echoed The compiler was able to make an intelligent guess that the closing parenthesis was probably missing and that insertion of the missing closing parenthesis would probably prevent the detection of more extraneous errors The insertion was therefore made but the user will have to fix the problem before the model can be generated MISSING TOKEN INSERTED BY PARSER gt This error indicates that something other than a comma was encountered when the syntax for ASSIST requires a comma The token found instead of the comma is echoed The compiler was able to make an intelligent guess that the comma was probably missing and that insertion of the missing comma would probably prevent the detection of more extraneous errors The insertion was therefore made but the user will have to fix the problem before the model can be generated MISSING TOKEN INSERTED BY PARSER gt This error indicates that something other than a semicolon was encountered when the syntax for ASSIST requires a semicolon The token found instead of the semicolon is echoed The compiler was able to make an intelligent guess that the semicolon was probably missing and that insertion 76 of the missing semicolon would probably prevent the detection of more extraneous errors The insertion was therefore made but the user will have to fix the problem before the model can be gen
94. ections Using the PRUNEZIF statement to reduce model size is discussed and demonstrated in section 4 1 13 Model Reduction Techniques Modeling the failure behavior of a complex system with many interacting components can produce a system state explosion that results in huge models with hundreds of thousands of states that cannot be 27 held or solved on typical computer systems This problem has been called the large state space prob lem However prudent use of various model reduction techniques with ASSIST allows the user to represent many such systems with reasonably sized models This section describes the model reduction techniques available in ASSIST For a demonstration of these techniques and a discussion of their effectiveness see reference 6 13 1 Model Pruning A model of a system with numerous components can have many long paths with one or two failures of each component type before a system failure condition is reached Because the occurrence of so many failures is unlikely during a short mission these long paths typically contribute insignificant amounts to the probability of system failure The dominant system failure modes are typically the short paths to system failure that have failures of like components Model pruning can be used to eliminate the long paths by conservatively assuming that system failure occurs earlier on those paths Model pruning is supported in ASSIST by the PRUNEIF statement whic
95. een IF and ENDIF or between FOR and ENDFOR The limit can be increased The default is e 100 for workstations and e 50 for the IBM PC SCRATCH EXPRESSION STORAGE OVERFLOW SPECIFY E OPTION id gt This error is the VMS equivalent of the previous error SEMICOLON CHANGED TO COMMA BY PARSER gt This error indicates that ASSIST found a semicolon but was able to guess that the user meant to use a comma instead The change was made in an attempt to limit the number of extraneous errors during continued parsing of the statement in error SEMICOLON EXPECTED id gt This error indicates that something other than a semicolon was encountered when the syntax for ASSIST requires a semicolon The token found instead of the semicolon is echoed If the semi colon was missing before the end of the file then the message end of file will be printed to the right of the colon SKIPPING EXTRANEOUS TOKENS id gt This error indicates that previous errors prevented continued parsing of part or all of the current statement Fix the other errors in this statement and this error should disappear SPACE STATEMENT IS MISSING gt This error indicates that the first rule was encountered yet the required SPACE statement was absent SPACE STATEMENT OVERFLOW SPECIFY PIC OPTION id gt This error indicates that there were more state space variables
96. erated MISSING TOKEN INSERTED BY PARSER gt This error indicates that something other than an equals sign was encountered when the syntax for ASSIST requires an equals sign The token found instead of the equals sign is echoed The com piler was able to make an intelligent guess that the equals sign was probably missing and that insertion of the missing equals sign would probably prevent the detection of more extraneous errors The insertion was therefore made but the user will have to fix the problem before the model can be generated MISSING TOKEN INSERTED BY PARSER OF gt This error indicates that something other than an OF key word was encountered when the syntax for ASSIST requires an OF key word The token found instead of the OF key word is echoed The compiler was able to make an intelligent guess that the OF key word was probably missing and that insertion of the missing OF key word would probably prevent the detection of more extraneous errors The insertion was therefore made but the user will have to fix the problem before the model can be generated MISSING TOKEN INSERTED BY PARSER gt This error indicates that something other than a closing bracket was encountered when the syntax for ASSIST requires a closing bracket The token found instead of the closing bracket is echoed The compiler was able to make an intelligent guess that the closing bracket was
97. eric item numeric item pow op factor bin numeric item lt sign op gt numeric item non index single item index variable unsigned value named constant cat op bin numeric item numeric function invocation numeric expression MOD CYC DIV 62 inc op cat op iae lt boolean function invocation gt lt function invocation gt numeric function invocation lt function invocation gt function invocation Ximpl func name function name lt expression list gt built in name lt built in expr list gt non index single item lt named constant gt named constant whole expression named constant lt whole expression gt lt whole expression gt lt state space var gt lt state space var gt lt whole expression gt state space var lt whole expression gt whole expression function name identifier impl func name identifier built in name SQRT EXP LN SIN COS TAN ARCSIN ARCCOS ARCTAN FACT SUM COUNT COMB PERM ABS ANY ALL SIZE MIN MAX truth value FALSE TRUE lt comment gt i text text under dollar lt E char gt E e D d letter A B C iD JE F G jH iI J K iL iM IN O P iQ IR iS T U iV iW iX Y Z a b c d e
98. error indicates that the built in function reference had more parameters passed than were expected See section 3 1 8 for details on the built in functions TOO MANY OPEN FILES CANNOT OPEN PLEASE CONTACT SYSTEM MANAGER filename gt This error indicates that an attempt was made to open the file but too many files were already open The user may have files open from suspended or background processes Try logging out of all your processes and logging back in If that does not work or you get this error repeatedly con tact your system manager about having your limits increased I TOO MANY SUBSCRIPTS ONLY SINGLY OR DOUBLY SUBSCRIPTED ARRAYS ARE ALLOWED id This error indicates that an illegal attempt was made to declare an array with more than two dimensions Triply subscripted arrays are not allowed by ASSIST TOO MANY SUBSCRIPTS THIS IS A SINGLY SUBSCRIPTED ARRAY arrayname gt This error indicates that a singly subscripted array was referenced with more than one subscript Check for consistency with the declaration of the array IRIPLE BOOLEAN EQUALITY NOT SUPPORTED USE A B AND B C INSTEAD OF A B C ETC token gt This error indicates that the user tried to use triple Boolean equality without the use of the key word AND The fix should be clear from the message TRIPLE EQUALITY NOT SUPPORTED USE A B AND B C INSTEAD OF A B C ETC token gt T
99. es count WARM pool warm Failed spares count WARM pool warm Spares count COLD pool cold Total active failed in triad Total active working in triad riad NWS hot NFS hot NWS warm NFS warm NS cold otal spares available to triad hot NFS hot NWS warm NFS warm NS cold NWS hot NFS hot NWS hot NS hot NFS hot NS hot IMPLICIT NS warm NWS warm NFS warm NWS warm NFS warm IMPLICIT PRW warm NWS warm N IMPLICIT PRF warm NWS warm N START NI triad NSI hot FS warm FS warm NFS warm NS warm NWS warm NS warm Count of working in triad Working spares count HOT pool hot 48 0 Failed spares count HOT pool hot NSI warm Working spares count WARM pool warm 0 Failed spares count WARM pool warm NSI cold Spares count COLD pool cold cede Sele decode dee Te kc cec Kc e Se KG te ede tele Fe x te G X KKK KKK KKK KKK KKK KKK KKK KKK kck ck ckck kk kk kk COMPONENT triad KKK KKK KKK KKK KKK KKK KK KKK KKK KKK KKK ck ck ck kk KKK KKK KKK KKK KKK KKK ck ckckckck ck ck ck ck ck ck kk IF NW triad O0 TRANTO NW triad BY NW triad L P triag Permanent fault arrival IF TFA triad 0 TH IF NS hot 0 TH IF NWS hot gt 0 RANTO NWS hot NW triad BY FAST PRW hot DEL hot IF NFS hot gt 0 R
100. es that something other than a comma was encountered in the parameter list for a built in function when the syntax for ASSIST requires a comma The token found instead of the comma is echoed This error usually occurs when a list function such as SUM COUNT MIN MAX ANY or ALL is invoked without any parameters COMMA EXPECTED func REQUIRES EXACTLY num PARAMETERS AND NO FEWER gt This error indicates that something other than a comma was encountered in the parameter list for a built in function when the syntax for ASSIST requires a comma The token found instead of the comma is echoed This error usually occurs when one or more parameters for the named function are missing 68 COMMAND LINE OPTION TOO BIG wid nnn limit 256 gt This error indicates that the user tried to specify the maximum width of an input file line to be greater than 256 Input lines are usually limited to wid 80 or 79 characters The user can increase the allowed width but not to a value greater than 256 COMMAND LINE OPTION TOO BIG wid nnn limit 256 gt This error is the VMS version of the previous error message COMMAND LINE OPTION TOO TINY wid nnn limit 38 This error indicates that the user tried to specify the maximum width of an input file line to be less than 38 Input lines are usually limited to wid 80 or 79 characters The user can decrease the allowed width
101. generate a cross reference map on the log file This cross reference map can be 69 used to help determine if the user s indentation style is inconsistent and can help the user to deter mine where the missing ELSE or ENDIF belongs EOF REACHED BEFORE NESTED RULE SEQUENCE TERMINATED ENDFOR MISSING gt This error indicates that no matching ENDFOR was found for a FOR The user should use the xref option to generate a cross reference map on the log file This cross reference map can be used to help determine if the user s indentation style is inconsistent and can help the user to deter mine where the missing ENDFOR belongs EOF REACHED BEFORE QUOTED TEXT TERMINATED on line nnn gt This error indicates that the matching quote to end quoted text on the specified line is missing This usually indicates that a prompt message in an INPUT statement or a SURE statement was never completed due to omission of the terminating quote character EQUAL SIGN EXPECTED token gt This error indicates that something other than an equals sign was encountered when the syntax for ASSIST requires an equals sign The token found instead of the equal sign is echoed EXP X VALUE IS TOO BIG real gt real expression on line linenumber gt This error indicates that during rule ge
102. greater in absolute magnitude than 1 0 The user should examine the log file to check the expression for mistakes and check the ASSIST input file rule sec tion for correctness e ARCCOS X ARGUMENT MUST BE 1 0 lt X lt 1 0 expression on line linenumber gt This error indicates that during rule generation an expression that was passed to the built in func tion ARCCOS evaluated to a number greater in absolute magnitude than 1 0 The user should examine the log file to check the expression for mistakes and check the ASSIST input file rule sec tion for correctness ARCSIN X ARGUMENT MUST BE 1 0 lt X lt 1 0 real ABS 1 0 expression on line linenumber gt This error indicates that during rule generation an expression that was passed to the built in func tion ARCSIN evaluated to real a number greater in absolute magnitude than 1 0 The user should examine the log file to check the expression for mistakes and check the ASSIST input file rule sec tion for correctness ARCSIN X ARGUMENT MUST BE 1 0 lt X lt 1 0 expression on line linenumber gt This error indicates that during rule generation an expression that was passed to the built in func tion ARCSIN evaluated to a number greater in absolute magnitude than 1 0 The user should examine the log file to check the expression for mistakes and check the ASSIST input file rule sec tion f
103. gt lt SPACE stat gt setup stat seq start stat seq START stat start stat seq rule stat seq any setup sec staL setup stat esego any sLart sec stat lt start stat seq gt any rule sec stat any rule sec stat rule stat seq global stat lt pre rule global stat gt lt global stat gt lt pre rule global stat gt dep variable def function def impl function def global stat XASSERT stat DEATHIF stat PRUNEIF stat lt TRANTO stat gt IF stat lt FOR stat gt quoted SURE stat constant def stat option def stat lt INPUT stat gt lt debug stat gt command option stat empty stat any sotup sec stot lt any slart sec stat gt any rule sec stat lt SPACE stat gt lt START stat gt lt sensitive keyword gt built in func name 56 sensitive keyword lt pre defined constant gt lt descriptive operator gt statement name option def name constant def stat const var def clause pre defined constant descriptive operator statement name BY FAST THEN ELSE ENDIF ENDFOR WITH OF IN ARRAY ON OFF FULL BOOLEAN option def AUTOFAST name TRIMOMEGA TRUE FALSE AND OR NOT MOD CYC DIV option def C OPTION DEBUG INPUT SPACE FUNCTION IMPLICIT VAR
104. gt lt const var def clause gt j START lt spac xpression gt gt ASSERT lt boolean expression gt DEATHIF lt boolean expression gt PRUNEIF PRUNIF lt boolean expression gt lt boolean expression gt IF boolean expression lt TRANTO clause gt lt TRANTO clause gt j IF lt boolean expression gt THEN rule stat seq ENDIF IF boolean expression THEN rule stat seq ELSE rule stat seq ENDIF FOR lt for range gt lt rule stat seq gt ENDFOR 58 quoted SURE stat lt command option stat gt lt debug stat gt lt empty stat gt lt TRANTO clause gt lt flag status gt lt input list gt lt input item gt lt prompt message gt lt function parm list gt lt index parm list gt lt impl parm list gt lt quot text gt lt quot text char gt lt space expression gt lt quot text gt C_OPTION identifier C_OPTION lt identifier gt lt value gt DEBUG DEBUG identifier TRANTO lt space destination list gt BY lt rate expression gt TRANTO lt rate expression gt OFF ON FULL input item input item lt named constant gt prompt message BOOLEAN BOOLEAN M M quot text lt identifier gt lt identifier gt lt identifier gt lt identifier gt lt state space var gt lt state space var gt quot tex
105. gt set range list lt index variable gt lt whole expression gt index variable IN lt whole expression gt lt set gt lt set range list gt lt i range gt lt whole expression gt lt i range gt lt i range list gt lt i range gt lower bound upper bound range bound lt rate expression gt lt lower bound gt upper bound lt range bound gt lt range bound gt whole expression lt real expression gt lt lt real expression gt lt real expression gt gt 60 expr list with of expression list built in expr list lt wild sub array gt lt expr gt whole or boolean expression lt whole expression gt lt real expression gt integer expression lt boolean expression gt lt bool term expr gt lt bool term gt lt bool factor gt lt bool item gt numeric comparison simple bool item lt lt real expression gt lt real expression gt gt FAST lt real expression gt lt real expression gt lt expr gt lt whole expression gt OF lt expr gt lt expr gt expr list with of lt whole expression gt OF lt expr gt expr list with of lt expr gt lt expr gt lt expression list gt lt expr gt lt expr gt lt built in expr list gt lt wild sub array gt lt wild sub array gt built in expr list named constant Dow
106. h subroutines functions PROCESS state trim fast in error is ignored when trimming is off IF state already present is a death state if flagged as suc ELSE save current state and dependent variable values hat are referenced in PRUNEIF sections for state printing WARNING message if a test fails THEN recompute dependent variables t ASSERT test all ASSE test al DEAT IF not a death DEATHIF RT s HIF s test all P RUNE E restore current state and dependen IF death or prune state AND print warning message and th EN ENDIF IF d st DIFs eath state AN deat erefore may no D lumping TH at number ELSE st IF prune stat e HEN fas Model contains recovery t be EN at number ELSE st ELSE LE IF trim AND ate number amp trim not being 1 death state flag the stat EN IF DIF state does n EN ENDIF RETU ENDFUNC DIF prun stat trimming is umped THEN e ot yet exist RN state number AIN process the start state compute oe start state rate the model gen 23 on State number THEN main algorithm ready list lt pointer to first state FOR cur IF comp rent state IN state is not set
107. h as identifiers and expressions The ASSIST statements themselves are then described in the second subsection 12 1 Language Building Blocks This section introduces the syntax for the identifier names numeric and Boolean expressions and built in functions that are the basic building blocks of the ASSIST input language 12 1 1 Identifiers An identifier is a name that is assigned to a constant or variable in the language All identifiers must begin with a letter and contain letters digits or underscored characters The following are valid identifiers A ABC PL MU_TRIAD X123 An ASSIST identifier must not exceed 28 characters Identifiers used for named constants that will be passed to SURE must be unique in the first 12 characters Constant array names should generally not exceed eight characters Section 3 2 1 Setup Section discusses constant definitions and gives more details on the limitations of constant array names The following are invalid identifiers 6A identifiers must begin with a letter 0X identifiers must begin with a letter A 2 special characters are not allowed A 3 embedded whitespace and newlines ar 12 1 2 Numeric Expressions illegal A numeric expression is any mathematical expression that produces either an integer or a real num ber when evaluated A numeric expression may contain literal values named constants state space vari ables index variables and arithmetic operations A
108. h is described in section 3 2 7 The pruning conditions are described by PRUNEIF statements much like the death con ditions are described using DEATHIF statements Like the death states the pruned states are lumped according to which PRUNELIF statement was satisfied by the state Since the model is truncated by assuming system failure when the pruning criterion is met this method is conservative The system failure states caused by model pruning are lumped together accord ing to the PRUNEIF statement that is satisfied thus the contribution to system failure probability caused by pruning can be determined easily from the SURE output file 13 2 Model Trimming A new method for reducing the size of semi Markov reliability models was recently developed by Dr Allan White and Daniel Palumbo of NASA Langley Research Center The details of this trimming method and the theorem proving that this method is conservative are given in reference 7 The user should read this paper to determine the system characteristics for which this trimming method is guaran teed to be conservative Not all systems can be trimmed The TRIM statement is used in the setup or start section of the ASSIST input file to trim the model The syntax is TRIM OFF or TRIM ON WITH lt trimomega gt or TRIM FULL WITH lt trimomega gt where lt trimomega gt is a real expression for the trimming bound Q im The fi
109. hether or not the source and destination state nodes of a transition are written to the model output file as an ordered n tuple in comments The default is COMMENT ON If the SPACE statement has a great number of state space variables it will take many characters on a line to print the state node In such instances ASSIST will force COMMENT OFF regardless of what the user requested When COMMENT is ON but is forced OFF because of length a warning message is generated To suppress the warning add COMMENT OFF statement to the input file Use of COMMENT FULL is equivalent to COMMENT ON The ECHO option controls whether or not the input file lines are echoed to the standard error file If set to ON the input file lines are echoed If the model file must contain the echo option the state ment must be a SURE statement included in quotes as in ECHO 1 Use of ECHO FULL is equivalent to ECHO ON The ON ED EATH option controls the number of death states in the model If reset to OFF then each distinct death state will be enumerated as a separate death state in the SURE model output file In some models thousands of different death states will result The default is ONEDEATH ON which forces the lumping of all death states according to the first DEATHIF statement to which that state conformed State 1 will contain all death states satisfying the first DEATHIF state 2 will contain all death st
110. his error indicates that the user tried to use triple equality without the use of the key word AND The fix should be clear from the message TRIPLE INEQUALITY NOT SUPPORTED USE A lt B AND B C INSTEAD OF A B C ETC token gt This error indicates that the user tried to use triple inequality without the use of the key word AND The fix should be clear from the message TYPE MISMATCH arrayname num IS A BOOLEAN SSV gt This error indicates that the user tried to do arithmetic with a Boolean state space variable This is usually undesirable but in those instances when it is useful the COUNT function is available to convert the Boolean state space variable to an integer value TYPE MISMATCH arrayname num IS AN INTEGER SSV gt This error indicates that the user tried to test an integer state space variable as if it were a Boolean This is usually undesirable but in those instances when it is useful the user can test for ssy lt gt 0 TYPE MISMATCH id gt This error indicates that two incompatible types were mixed in the same expression or the wrong value type was used for the context TYPE MISMATCH id IS A BOOLEAN SSV gt This error indicates that the user tried to do arithmetic with a Boolean state space variable This is usually undesirable but in those instances when it is useful the COUNT function is available to convert the Boolea
111. hort paths to system failure 26 consisting of like component failures Model pruning can eliminate the long paths to system failure if one conservatively assumes that system failure occurs earlier on those paths The PRUNEIF statement can be used to truncate the Markov model automatically Assume that the probability of more than M component failures occurring during a mission is negligible compared to the probability of system failure Using NCF as a state space variable to represent the number of component failures the following statement appropriately truncates the model PRUNEIF NCF gt M The model is truncated by assuming system failure when the truncation criteria are met This method is therefore conservative Note that the number of aggregated pruned states reported by ASSIST is actually the number of transitions that resulted in a pruned state not the number of unique state n tuples that are pruned states The PRUNEIF statement specifies which states are pruned states conservatively assumed to be absorbing states in the model that reduce the total model size The PRUNEIF statement has the same syntax as the DEATHIF statement PRUNEIF condition The condition is a Boolean expression with optional parentheses The alternate spelling PRUNIF is also allowed Consider the following example SPACE DIM1 2 4 DIM2 3 5 PRUNEIF DIM1 4 OR DIM2 3 This statemen
112. hould examine the log file to check the expression for mistakes and check the ASSIST input file rule section for correctness ARITHMETIC REAL OVERFLOW real real expression on line linenumber gt This error indicates that during rule generation the product of two real numbers exceeded the maximum or minimum value allowed by the hardware The user should examine the log file to check the expression for mistakes and check the ASSIST input file rule section for correctness ARITHMETIC OPERATOR IN A BOOLEAN EXPRESSION op gt This error indicates that the user tried to do arithmetic on Boolean quantities If the user desires to do arithmetic with the ordinal value of a Boolean then the COUNT function must be used to con vert the Boolean to an integer Arithmetic on Booleans is otherwise disallowed ARRAY DIMENSION OUT OF BOUNDS expression on line linenumber gt This error indicates that during rule generation the expression for a subscript of an array evalu ated to a value that was not within the declared range For example if the array is bounded 5 11 and referenced with an expression evaluating to 12 then this error will occur The user should examine the log file and check the expression for mistakes and check the ASSIST input file rule section for correctness ARRAY DIMENSION OUT OF BOUNDS token gt This error indicates that during parsing the constant expression for a subscrip
113. iables can be put in an array and the FOR construct can be used to define several TRANTO or DEATHIF rules at once Do not think of the FOR construct as a loop in the procedural sense Think of it as repeatedly generating a set of rules The syntax of a FOR construct is FOR lt index gt IN lt set gt lt more rules gt ENDFOR 24 The old FOR construct syntax which specified a single index range with the lower and upper bounds separated by a comma is still supported but the new syntax is recommended for clarity The formal syntactical description of the old form therefore is relegated to the appendix A FOR construct generates rules over a set of values A set in the ASSIST language is a collection of whole numbers The numbers can be listed individually or specified via ranges The syntax of a set is lt expression gt expression expression expression The ellipsis indicates a value range beginning with the left value and ending with the right value inclusively Thus 5 9 specifies the numbers 5 6 7 8 9 whereas 5 9 specifies the numbers 5 and 9 Examples of sets are 3 L5 1 5 5 1 3 5 0 4 6 9 1 4 NP 5 NP 4 NP 5 NP 1 Consider a system in which system failure occurs when at least half of any of three types of compo nents are faulty An array NA of range 1 to 3 could represent the number of each type of component active in the system and an arr
114. ile anywhere before the SPACE statement This warning message appears when two or more levels of error reporting are requested LH ELLIPSIS AND UPPER BOUND ARE MISSING USING 1 num gt This warning indicates that the user forgot to specify both a lower and an upper bound for either an array subscript or the value range for a state space variable ASSIST had to assume what the user meant The assumption for example was that ARRAY 2 OF 5 was supposed to read ARRAY 1 2 OF 1 5 Since the assumption may not always be correct the user should specify the full legal syntax and specifically say what is meant This serious warning message appears when one or more levels of error reporting are requested EMPTY LIST SPECIFIED gt This warning indicates that the user followed a left parenthesis by a right parenthesis or a left bracket by a right bracket It could also indicate that an INPUT statement did not specify any con stants to be input that a SPACE statement did not have any state space variables or that a TRANTO did not list any destination expressions The enclosed text may be in 1 2 This serious warning message appears when one or more levels of error reporting are requested IDENTIFIER TRUNCATED 28 CHARS MAX gt This warning indicates that the identifier in question was truncated to 28 characters in length The arrow points to
115. ing of Detected Warnings The w lt level gt command line option is used to specify the number of levels of warning report ing All warnings at a level less than or equal to the requested number of reporting levels are printed to the standard error file and to the log file The default is four levels of warning reporting A list of all warning levels in ASSIST appears in table C1 Table C1 ASSIST Warning Levels Level Description 0 No warnings whatsoever Same as w none The Serious level These warnings are major Same as w fewer 1 2 The Default level These warnings are usually worth noting 3 The Minor level These warnings are less major Same as w all 87 An alphabetical listing of all warning messages follows ASSERTION FAILED token gt This warning indicates that an invariant or other assertion failed because of a certain model state The state node for the current state and the log file line number corresponding to the failed ASSERT condition are printed following the warning message This serious warning message appears when one or more levels of error reporting are requested COMMENT OPTION TURNED BACK OFF DUE TO EXCESSIVE STATE SPACE VARIABLI COUNT id gt This warning indicates that since the state space is so large ASSIST refuses to allow the COMMENT option to be ON To get rid of this message add the statement COMMENT OFF to the ASSIST input f
116. inition nonconstant If the definition is for a variable then the user should consider the use of an IMPLICIT or FUNCTION definition See section 3 2 7 for a description of the rule section and sections 3 2 3 and 3 2 4 for details on IMPLICIT and FUNCTION definitions respectively I STATEMENT NOT VALID IN THIS SECTION id This error indicates that a statement is out of sequence Move the statement to its proper location and the error will disappear STATEMENT OUT OF SEQUENCE NOT ALLOWED IN RULE SECTION gt This error indicates that a statement is out of sequence Move the statement to its proper location and the error will disappear The setup start and rule sections are described in sections 3 2 1 3 2 2 and 3 2 7 respectively They are listed in the BNF description in appendix B LH STATEMENT OUT OF SEQUENCE NOT ALLOWED IN SETUP SECTION gt This error indicates that a statement is out of sequence Move the statement to its proper location and the error will disappear The setup start and rule sections are described in sections 3 2 1 3 2 2 and 3 2 7 respectively They are listed in the BNF description in appendix B I STATEMENT OUT OF SEQUENCE NOT ALLOWED IN START SECTION gt This error indicates that a statement is out of sequence Move the statement to its proper loca
117. is replaced with a cold spare processor if one is available There is no fault detection for spare processors until they become active This architecture can be described in the ASSIST input language as follows TRIAD WITH COLD SPARES N PROCS 3 Number of active processors N SPARES 2 Number of spare processors LAMBDA P 1E 4 Failure rate of active processors 34 LAMBDA S 1E 5 Failure rate of spare processors DELTA 3 6E3 Reconfiguration rate SPACE NP 0 N_PROCS Number of active processors FP 0 N PROCS Number of failed active processors S 0 N SPARES Number of spare processors FS 0 N SPARES Number of failed spare processors START N PROCS 0 N SPARES 0 DEATHIF 2 NFP NP IF NP NFP RANTO NFP NFP 1 BY NP NFP LAMBDA P Active processor failure IF NS NFS RANTO NFS NFS 1 BY NS LAMBDA 3 Spare processor failure IF NFP gt 0 AND NS gt 0 THEN IF NS gt NFS Replace failed processor with working spare RANTO NP NFP 1 NS 1 NFS BY FAST 1 NFS NS NFP DELTA IF NFS gt 0 Replace failed processor with failed spare RANTO NP NFP NS 1 NFS 1 BY FAST NFS NS NFP DELTA ENDIF The TRANTO statements describe the three transition types possible between states in the semi Markov model e
118. is to present a real ambiguity then the warning will be changed to an error and users will have to change their input files The documentation in section 3 1 2 indicates that the decimal point is required to reserve the right to extend the language in the future This minor warning message appears when three or more levels of error reporting are requested NUMBER STRING TRUNCATED 27 CHARS MAX gt This warning indicates that a number string was too long and therefore was truncated If a preci sion digit was lost then the problem is minimal If an exponent digit was lost then the problem is serious This serious warning message appears when one or more levels of error reporting are requested OLD SYNTAX SPECIFIED PLEASE REPLACE WITH NEW SYNTAX gt This warning indicates that the user is using the old syntax for a construct The old syntax is still legal hence the warning only appears when users ask for all warnings The old syntax for the FOR 89 construct can be ambiguous in the user s mind if that user is using both the old and new syntax in different ASSIST input files For example III 1 3 for the old syntax includes the number 2 in the range whereas the new syntax III IN 1 3 does not include the number 2 This minor warning message appears when three or more levels of error reporting are requested OPTION ONLY VALID ON A UNIX SYSTEM OPTION IGNORED opt gt Cert
119. ise fals OR true when either sid otherwise fals XOR true when only one side is true otherwise fals NOT true when right side is false false when right side is true Optionally an ampersand can be used instead of the word AND and a vertical bar can be used instead of the word OR See the language syntax in appendix B for details on the use of special sym bols Truth tables for the comparators are given in tables 11 through 4 Table 11 Truth Table for AND Conjunction AND TRUE FALSE TRUE TRUE FALSE FALSE FALSE FALSE Table 3 Truth Table for XOR Conjunction TRUE FALSE TRUE FALSE TRUE FALSE TRUE FALSE Table 2 Truth Table for OR Conjunction OR TRUE FALSE TRUE TRUE TRUE FALSE TRUE FALSE Table 4 Truth Table for NOT Conjunction P NOT FALSE TRUE TRUE FALSE 12 1 5 Arrays The ASSIST language supports the use of both singly and doubly subscripted arrays A singly sub scripted array is simply an ordered sequence of scalars A scalar is usually an integer or a real number but could also be a Boolean value The index number refers to the position in the sequence For exam ple index 3 corresponds to the third scalar in the sequence Consider the array ELE 5 11 22 17 4 37 99 2 The ELE array has eight scalars The third scalar is 22 To reference the third scalar in the array use ELE 3 The square brackets denote an index or subscript used to reference a
120. ite Allan L Upper and Lower Bounds for Semi Markov Reliability Models of Reconfigurable Systems NASA CR 172340 1984 Butler Ricky W and White Allan L SURE Reliability Analysis Program and Mathematics NASA TP 2764 1988 Butler R W An Abstract Specification Language for Markov Reliability Models NASA TM 86423 1985 Butler Ricky W and Stevenson Philip H The PAWS and STEM Reliability Analysis Programs NASA TM 100572 1988 Butler Ricky W and Johnson Sally C Techniques for Modeling the Reliability of Fault Tolerant Systems With the Markov State Space Approach NASA RP 1348 1995 Johnson Sally C Reliability Analysis of Large Complex Systems Using ASSIST A Collection of Technical Papers AIAA IEEE 8th Digital Avionics Systems Conference Part 1 Oct 1988 pp 227 234 Available as AIAA 88 3898 White Allan L and Palumbo Daniel L State Reduction for Semi Markov Reliability Models Proceedings of the Annual Reliability and Maintainability Symposium IEEE 1990 pp 280 285 Johnson S C and Butler R W A Table Oriented Interface for Reliability Modeling of Fault Tolerant Architectures Proceedings of the IEEE AIAA 11th Digital Avionics Systems Conference 1992 pp 149 154 Palumbo D L Using Failure Modes and Effects Simulation as a Means of Reliability Analysis Proceedings of the IEEE AIAA llth Digital Avionics Systems Conference 1992 pp 102 107 96 Form
121. k ck ck KK KKK KKK KKK KEK KKK KKK KKK KKK KKK ck ck ck KK KK K KK K MISC DEATH amp PRUNE kk kk kk ck CckCckckckckckckckckck ckckckckckck ckckckck ck kck ck ck ck kk KKK KKK KKK KKK KKK KKK KKK KKK kck ck ck ck kk DEATHIF TFA_triad gt TWA_triad 16 8 Triad With Hot Warm Cold Spares The next example is a triad with hot warm and cold spares The three processors in the triad have permanent fault arrival rates of p If available hot spares are taken first warm next and cold last Faulty processors are replaced with spares at fast exponential rate bot PU Scola Failure rates for hot and warm spares are given by A and X respectively Cold spares are optimistically assumed to have failure rates of zero hot warm KKK KKK KKK KKK KK KKK ckckck ck ck ck kk kk ck Cckckckckckckckckckckckckckckck ckckck ck ck ck ck kc kk aK aK KEK RATE CONSTANTS KEK aK aK KKK KKK KKK KKK KK KKK KK ck ck ck ck kk kk KKK KKK KKK KKK KK KKK ck ckck ck ck ck ck ck kk 47 _P_triad EL hot F warm EL cold J yy LAM_hot LAM_warm NI_triad NSI_hot NSI_warm NSI_cold SPACE W_triad WS hot FS hot WS warm FS warm S cold IMPLICI FA_ NI_t IMPLICI WA_ NW_t IMPLICIT TA_t IMPLICIT NS_t CST NWS ll PR NONE nd A 0 e KKK KKK KKK ll PON C Oc
122. kck ck ck ck ck ck kk R D triad 1 414e3 Rate to degrade for triad L I triad 0 707e4 Arrival rate of intermittent fault for triad ALP triad 2 718281e3 Rate benign triad intermittent goes active BET triad 3 141592e3 Rate active triad intermittent goes benign KKK KK KK KKK KKK KKK ck ckck ck ck ck kk kk KKK KKK ck ckckckckckckckckckck kckck ck ck ck kk kk kk kk KXK SPACE CONSTANTS KAK x x KKK KKK KKK KKK KK KKK KK ck ck ck KK KKK KKK KKK KKK KK KKK KKK KK ck ck ck ck kk kk NI triad 3 Redundancy count for triad NTOT NI_triad Total number of components initially CAR OR Re AER RA RK X RRA AR RRR UK OR KAR KY EERE REKEREKE AIR RR ERE RAK RRR KAR EK KY ERK aa EAX STATE SPACE DEFINED X EER ARA KEKR ROR RAIA A A KIER RA AOR KCK KDE ORE GARR RS AER AIA RAK TKR RR ARR KON KERERE SPACE W_triad 0 NI triad Count of working in triad FA_triad 0 NI triad Count of active failed in triad FB triad 0 NI triad Count of benign failed in triad i IMPLICI FA triad NFA triad Total active failed in triad NFA triad IMPLICI WA triad NW triad NFB triad Total active working in triad NW triad NFB_triad IMPLICI A triad NW triad NFB triad NFA triad Total active in triad TFA triad TWA triad
123. l expressions is dis cussed in appendix A 12 1 3 Numeric Precision The numeric precision of integer arithmetic in ASSIST is at least 32 bits The maximum integer value is 2147483647 The minimum integer value is 2147483648 Future ports to machines with 60 or 64 bit architectures may allow even larger integers The numeric precision of real number arithmetic in ASSIST is at least 12 significant digits The exponent size range is machine dependent and amounts to double precision on most 32 bit architectures and to single precision on most 60 or 64 bit architectures Currently ASSIST is supported only on 32 bit machines 12 1 4 Boolean Expressions A Boolean expression is any mathematical expression that evaluates to TRUE or FALSE A Boolean expression may contain numeric expressions plus relational operators and conjunctions There are two possible literal truth Boolean values TRUE or FALSE These values must be spelled out in an ASSIST input file and cannot be abbreviated even though ASSIST abbreviates them to T and F in comments when writing the model output file for SURE Valid relational operators that can be used in Boolean expressions are less than greater than lt less than or equal to gt greater than or equal to equal to lt gt not equal to Valid comparative operators that can be used in Boolean expressions are AND true when both sides ar otherw
124. literal value or number is a contiguous sequence up to 28 characters consisting of digits an optional decimal point and an optional signed or unsigned exponent that is preceded by the letter e The ASSIST language requires that each number begin with a digit The following are legal numbers The following are illegal numbers Tels only one decimal allowed d does not begin with a digit use 0 6 3 embedded blank not allowed within 1 instead a number Scientific notation 1s also allowed The letter e embedded in a literal numeric value denotes that an integer power of 10 follows For example the values of 6 023 x 102 4 111 x 10 133 are written in ASSIST as 6 023e23 4 111e 13 respectively Valid operations in numeric expressions are E addition a subtraction X multiplication real division DIV integer division for quotient MOD integer division for remainder CYC integer division for cyclically wrapped quotient x CYC y 1 x 1 MOD y AUR exponentiation 3 parentheses enclose operations to be performed first Operations within parentheses are always performed first Exponentiation is performed next with right to left associativity Multiplication and division including D1 next with left to right associativity Addition and subtraction are V MOD and CYC are performed performed next with left to right associativity The order of precedence used in ASSIST for evaluating mathematica
125. ly one START statement or an error message will be printed Three additional types of macro definitions are allowed in this section namely the FUNCTION IMPLICIT and VARIABLE definitions The definitions can occur in any sequence except that an identifier may not be referenced before it is defined 12 2 3 IMPLICIT Statement The IMPLICIT statement is used to define a quantity that is not in the state space itself but is a function of the state space The value of the implicit function is based upon constants and state space variables For example if NWP is a state space variable representing the number of working processors and NI is aconstant denoting the number of initial processors then the declaration IMPLICIT NFP NWP NI NWP defines NFP number of failed processors to be the difference between the initial number and the cur rent number of working processors The implicit function shown above can be referenced as illustrated in the following DEATHIF statement DEATHIF NWP NFP The syntax is IMPLICIT lt identifier gt lt state space variable list gt lt parameter list gt body The state space variable list consists of one or more state space variable name identifiers separated by commas The identifiers must already have been defined in a SPACE statement All state space vari ables that are referenced in the body of an IMPLICIT statement m
126. ly tedious and error prone The Abstract Semi Markov Specifi cation Interface to the Semi Markov Unreliability Range Evaluator SURE Tool ASSIST computer program allows the user to describe the semi Markov model in a high level language Instead of listing the individual model states the user specifies the rules governing the behavior of the system and these are used to generate the model auto matically A few statements in the abstract language can describe a very large complex model Because no assumptions are made about the system being modeled ASSIST can be used to generate models describing the behavior of any system The ASSIST program and its input language are described and illustrated by examples 10 Introduction Semi Markov models can be used to calculate the reliability of virtually any fault tolerant system New advances in computation such as the Semi Markov Unreliability Range Evaluator SURE pro gram enable the accurate solution of extremely large and complex Markov models refs 1 and 2 In this paper the term Markov will be used to refer to both Markov and the more general semi Markov models However the generation by hand of the large models needed to capture the complex failure and reconfiguration behavior of most realistic fault tolerant architectures has been an intractable prob lem Many of the early fault tolerant architectures are relatively simple to model Even the early com plex systems usually had subsy
127. micolon The previous example could also have been specified as follows INPUT Enter failure rate of a processor LAMBDA Enter rate to reconfigure in a spare DELTA 12 in which case the prompt messages would read Enter failure rate of a processor Enter rate to reconfigure in a spare More generally the syntax of an input item in the input list is lt identifier gt or prompt lt identifier gt Each entered value or expression must be terminated by a semicolon Because expressions can span more than one line pressing the return key is not a substitute for a semicolon Failure to enter a semi colon will cause ASSIST to wait until one is typed in A Boolean constant can also be input The method is to precede the identifier name with the word BOOLEAN in the INPUT statement For example INPUT BOOLEAN FLAG INPUT Enter the flag BOOLEAN FLAG resulting in respective prompts FLAG Enter the flag 12 2 1 4 Comments Comments in ASSIST must either be initiated with and terminated with or be initiated with a left curly bracket and terminated with a right curly bracket p A comment may appear anywhere in the input where an extra space could occur A comment may not appear in the middle of a literal constant or an identifier For example the following are illegal PI 1 14 more decimals 15926 PI 1 14 more decimals
128. n VA 12a DISTRIBUTION AVAILABILITY STATEMENT 12b DISTRIBUTION CODE Unclassified Unlimited Subject Category 62 Availability NASA CASI 301 621 0390 13 ABSTRACT Maximum 200 words Semi Markov models can be used to analyze the reliability of virtually any fault tolerant system However the pro cess of delineating all the states and transitions in a complex system model can be devastatingly tedious and error prone The Abstract Semi Markov Specification Interface to the SURE Tool ASSIST computer program allows the user to describe the semi Markov model in a high level language Instead of listing the individual model states the user specifies the rules governing the behavior of the system and these are used to generate the model automat ically A few statements in the abstract language can describe a very large complex model Because no assump tions are made about the system being modeled ASSIST can be used to generate models describing the behavior of any system The ASSIST program and its input language are described and illustrated by examples 14 SUBJECT TERMS 15 NUMBER OF PAGES Reliability analysis Fault tolerant systems 101 16 PRICE CODE A06 17 SECURITY CLASSIFICATION 18 SECURITY CLASSIFICATION 19 SECURITY CLASSIFICATION 20 LIMITATION OF REPORT OF THIS PAGE OF ABSTRACT OF ABSTRACT Unclassified Unclassified Unclassified NSN 7540 01 280 5500 Standard Form 298 Rev 2 89 Prescribed by ANSI Std 239 18 298 1
129. n individual position or scalar value within the array Reference to the array name without the bracketed index indicates the whole array With the exception of a few built in array functions arithmetic can be performed only on scalars not on arrays Therefore the user must always use an index after the array name to indicate which array values to use in the arithmetic expression There are some built in functions that operate on entire arrays One example is the function SUM which when given an array name will return the sum of all array elements For example ARR 6 3 1 ARRSUM SUM ARR In the above example the array ARR contains three scalars The scalar constant ARRSUM is defined as the sum of all scalars in the array ARR This sum is 10 In this example the following are numeri cally equivalent ARRSUM 10 ARRSUM ARR 1 ARR 2 ARR 3 ARRSUM SUM ARR A doubly subscripted array is similar to a table or a matrix For example consider the table 17 38 24 12 15 28 11 99 54 37 29 44 66 102 13 Two index values are required to denote a scalar in a doubly subscripted table The first index gives the row and the second index gives the column The scalar represented by TABLE 2 5 has the value 37 The first index indicates that the value is in the second row The second index indicates that the value is in the fifth column The above array can be typed into an ASSIST input file as illustrated T
130. n state space variable to an integer value TYPE MISMATCH id IS AN INTEGER SSV gt This error indicates that the user tried to test an integer state space variable as if it were a Boolean This is usually undesirable but in those instances when it is useful the user can test for ssy lt gt 0 86 VALID ONLY IN RATE EXPRESSION CONCATENATION gt This error indicates that the concatenation operation is valid only in a rate expression Concatena tion can usually be replaced by specifying an array subscript inside square brackets This should fix the problem VARIABLE CANNOT BE REFERENCED IN BODY UNLESS LISTED IN STATE SPACE VARI ABLE LIST ssv gt This error indicates that an attempt was made to use a state space variable in the body of an IMPLICIT or FUNCTION definition without having declared it in the state space variable list for an IMPLICIT If the user is defining a FUNCTION it will have to be converted to an IMPLICIT in order to reference the state space variable See sections 3 2 3 and 3 2 4 for details I T VARIABLE STATEMENT CANNOT CONTAIN A FUNCTION PARAMETER LIST CONSIDER USING AN IMPILICT FUNCTION token gt This error indicates that a VARIABLE statement definition cannot have a parameter list following the state space variable list VARIABLES NOT ALLOWED IN CONSTANT DEFINITION E
131. name must end with an ast suffix A file without this extension cannot be processed by ASSIST When running ASSIST the user may omit the suffix when typing in the file name For example either of the following will process the file foo ast assist foo assist foo ast The syntax and semantics of the ASSIST instructions are described below in detail 15 1 1 Model File The model output file produced by the program contains the semi Markov model in the format needed for input to the SURE computer program The model file has a mod file extension The model file contains all the named numeric non Boolean constants defined in the ASSIST input file setup and start sections as well as in the transitions generated by the ASSIST rule section The ASSIST file layout and its three sections are discussed in the next chapter Any statements in the ASSIST input file that are surrounded by double quotation marks are also copied directly into the model file These statements and named constants appear in the model file in the same sequence in which they appear in the ASSIST input file Values input with the ASSIST INPUT statement are treated as named constants All the transitions between states defining the semi Markov model are listed next Each SURE state is defined by a unique integer To make the model easier to understand the model file is annotated with the state space variables of each state in comments which SURE will ignore For example
132. neration the value of x for exp was too big The value passed for x is printed to the left of the gt and the maximum value allowed is printed to the right of the gt EXPECT ON OFF FULL or id gt This error indicates that an option definition name was followed by something other than one of the legal choices listed in the message The user may have tried to redefine an option to be a named constant or a state space variable Option names can only appear in option definition statements EXPRESSION OPERAND LIST OVERFLOW SPECIFY O OPTION id gt This error indicates that a very long expression was being parsed The expression was longer than ever anticipated If the expression cannot be simplified then increase the allowable size with the o num command line option or in a C_OPTION O num statement as the first line of the input file The default is o 100 for workstations and o 50 for the IBM PC EXPRESSION OPERAND LIST OVERFLOW SPECIFY O OPTION id gt This error is the VMS equivalent of the previous error EXPRESSION REQUIRED BUT WAS OMITTED token gt This error indicates that something other than an expression was encountered when the syntax for ASSIST requires an expression The token found instead of the expression is echoed Gl FILE NAME TOO LONG gt This error indicates that the name of at least one of the ASSIST file names is too long Remember
133. nf FACT n lt O0 expression on line linenumber gt This error indicates that during rule generation a negative number was computed and passed to the built in function FACT The user needs to check the input file for an incorrect specification of the model The expression that caused the problem can be most quickly located by examining the log file NEGATIVE VALUES NOT ALLOWED USE A WHOLE NUMBER int PERM n lt 0 expression on line linenumber gt This error indicates that during rule generation a negative number was computed and passed to the built in function PERM The user needs to check the input file for an incorrect specification of the model The expression that caused the problem can be most quickly located by examining the log file NOT ALLOWED IN IMPLICIT DEFINITION BODY ONLY STATE SPACE VARIABLES NAMED CONSTANTS OR LITERALS MAY BI INHERITED id This error indicates that the indicated identifier could not be used in the body of an implicit defini tion It was probably used as a parameter in a previous FUNCTION or IMPLICIT It might be a state space variable that was used in the body but not listed in the state space variable list LH NOT YET IMPLEMENTED gt This error indicates that the user tried to use a future option of a pending version of ASSIST that is still under development and no
134. nger than allowed Prompt messages should be brief yet clear A prompt message may not have more than 90 characters PROMPT STRING OR IDENTIFIER EXPECTED foken This error indicates that something other than a prompt string or identifier was encountered in an INPUT statement when the syntax for ASSIST requires a prompt string or identifier The token found instead of the prompt string or identifier is echoed QUITTING COMPILATION gt This error indicates that ASSIST was unable to continue processing the input file because of an inability to correct for previous errors The user should fix all known errors and this error will disappear RANGE IS TOO WIDE DIFFERENCE UPPER LOWER LIMITED BY 255 min max gt I This error indicates that the range specified by the user is too wide Only 256 dimension slots are allowed inclusive of both end points of the range The user must make min and max closer together 80 RANGE IS TOO WIDE DIFFERENCE UPPER LOWER LIMITED BY 32767 min max This error indicates that the range specified by the user is too wide Only 32767 values are allowed inclusive of both end points of the range The user must make min and max closer together RATE EXPRESSION MUST BEGIN WITH KEYWORD BY token gt This error indicates that the destination clause of a TRANTO statement was finished but no BY followed the clause This
135. not for the START state The syntax of a space expression item is lt expr gt OF lt expr gt or lt space expression gt Positional and assigned descriptions cannot be mixed in the same statement When assigned values are used the parentheses are not used and state space variables that do not change values need not be specified For example if the space is SPACE NP 0 6 NF ARRAY 1 3 OF 0 6 NX all the following TRANTO statements are equivalent IF NF 2 gt 0 TRANTO NP 1 NF 1 NF 2 1 NF 3 NX BY LAMBDA IF NF 2 gt 0 TRANTO NP 1 NF 2 1 BY LAMBDA IF NF 2 gt 0 TRANTO NP NP 1 NF 2 NF 2 1 BY LAMBDA 22 Notice that one does not have to specify state space variables in the destination state when the val ues do not change If however the positional form is being used then one must be careful to make sure that the correct number of commas separate the variables being changed Spaces around the punctuation are not necessary but have been added for clarity Because it is so common to increase or to decrease the value of a state space variable by one the and operations which add one and subtract one respectively are allowed in the destination field Consider the following two forms which have the same effect TRANTO NWP NWP 1 TRANTO NWP In addition to providing a convenient shorthand notation the and constructs are actually more efficiently implemented than
136. nt faults arrive at rate Ar 3 Transient faults disappear at fast exponential rate 6 40 4 Reconfiguration of processors with permanent faults or transient faults that remain long enough to be detected occurs at fast exponential rate 5 System failure occurs when a majority of the processors have permanent or transient faults The ASSIST input file that describes this system is as follows QUAD WITH TRANSIENT FAULTS NP 4 Number of processors LAMBDA P 1E 4 Permanent fault arrival rate LAMBDA T 10 LAMBDA P Transient fault arrival rate DELTA D 5 Transient fault disappearance rate DELTA R 3 6E3 o5 Reconfiguration rate SPACE NW O NP Number of working processors NFP O NP Active procs with permanent faults NET 0 NP Active procs with transient faults START NP 0 0 DEATHIF NFP NFT gt NW Majority of active processors failed IF NW gt 0 THEN TRANTO NW 1 NFP 1 BY NW LAMBDA P Permanent fault arrival TRANTO NW 1 NFT 1 BY NW LAMBDA T Transient fault arrival ENDIF IF NFT gt 0 THEN RANTO NW 1 NFT 1 BY FAST DELTA D Transient fault disappearance RANTO NFT BY FAST DELTA R Transient fault reconfiguration ENDIF IF NFP gt 0 TRANTO NFP BY FAST DELTA_R Permanent fault reconfiguration
137. ntifier is a function parameter then it must be listed in the parameter list between the parentheses LH PARAMETER COUNT OVERFLOW SPECIFY P OPTION id This error indicates that the parameter or state space variable list contained more than the maxi mum number of identifiers allowed Since the default is fairly large a function that exceeds it has so many parameters that it would probably be difficult to keep them straight The best solution is to try to have a larger number of smaller functions with fewer parameters The user can increase the parameter limit if necessary with the p2num command line option or in a C OPTION P num statement as the first line of the input file The default is p 64 for workstations and p 32 for the IBM PC 79 PARAMETER COUNT OVERFLOW SPECIFY P OPTION id gt This error is the VMS equivalent of the previous error PERMISSION DENIED NO ACCESS GRANTED PLEASE CONTACT SYSTEM MANAGER oo ast gt This error indicates that the user does not have permission to read the input file The user should talk to the owner of the file about gaining permission or contact the local system manager for help POSTFIX EXPRESSION STACK OVERFLOW SPECIFY O OPTION COMMAND LINI OPTIONS TOO BIG gt This error indicates that the user asked for more memory for the expression stack than all
138. om 0 through 255 Since large mod els may contain hundreds of thousands of states that must all be stored during rule generation ASSIST packs the values into as few bits as possible When explicit ranges are used only a required number of bits are used thus greatly decreasing the amount of memory needed to store the model Thus execution time speeds up because less page swapping of virtual memory is needed the state matching hashing algorithm is more efficient Checks are also made during rule generation and error messages are printed whenever a state is generated that contains a state space variable that is out of range as defined in the SPACE statement Thus for speed and model verification reasons the user is advised to give each state space variable an explicit range Examples of ranges and corresponding numbers of bits that are required to encode each range are listed in table 9 The number of bits required depends only upon the difference between the upper and lower bounds of a given range not upon the values themselves Table 9 Bits Required to Pack a State Space Variable BOOLEAN 0 1 0 2 0 3 0 4 0 7 0 8 0 15 0 16 33 34 101 116 RRP MnP BPwWwWN NY The SPACI CI statement marks the end of the setup section 15 12 2 2 Start Section The start section of the file contains more definitions plus a single START statement which can occur anywhere in the section There must be exact
139. ool scalar COUNTC list dim list Array Scalar size a dima 12 1 8 4 Array list functions The array list functions are listed in table 8 All array list functions operate on lists of arrays subarrays or scalars For example if Al A2 and A3 are arrays and if X Y and Z are scalars dim Al dim A2 dim A3 SUM A1 X Y A2 Z A3 Y aj X Y 4 Y az Z 4 Y a3 i l i l i l 8 where dim Ax is the dimension of Ax Note that the array functions operate on all array elements as if they had each been listed individually If an array is doubly subscripted all elements in the array table are operated upon For example if X is a 3 by 5 array then 3 5 SUM X b Ex i lj 1 The asterisk wild card can be used to limit summation within a doubly subscripted array to a single row or column as in 5 SUM X FOO X X25 T J 3 SUM X FOO X X z i 1 The new features in ASSIST revisions 7 0 and higher namely the combinatorial functions FACT factorial COMB combinatorial PERM permulation GAM gamma and the absolute value function ABS require revision 7 9 or greater of SURE STEM or PAWS in order to solve models using these features Model files produced with ASSIST 7 0 can be processed with older revisions of SURE STEM or PAWS provided that the new functions are not referenced 12 2 Language Statements This section describes the syntax for the statements that make up the A
140. or correctness 65 ARITHMETIC INTEGER OVERFLOW int int expression on line linenumber This error indicates that during rule generation the sum or difference of two integers exceeded the maximum or minimum value allowed by the hardware Most models use very small integers The user should examine the log file to check the expression for mistakes and check the ASSIST input file rule section for correctness ARITHMETIC INTEGER OVERFLOW int int expression on line linenumber gt This error indicates that during rule generation the product of two integers exceeded the maxi mum or minimum value allowed by the hardware Most models use very small integers The user should examine the log file to check the expression for mistakes and check the ASSIST input file rule section for correctness ARITHMETIC REAL OVERFLOW expression on lin linenumber gt This error indicates that during rule generation a value in a real expression exceeded the maxi mum or minimum value allowed by the hardware The user should examine the log file to check the expression for mistakes and check the ASSIST input file rule section for correctness ARITHMETIC REAL OVERFLOW real real expression on line linenumber This error indicates that during rule generation the sum or difference of two real numbers exceeded the maximum or minimum value allowed by the hardware The user s
141. ors can be used to convert a number to a Boolean For example 6 COUNT FLAG or I lt gt 0 respectively INVALID PROMOTION OF real TO integer This error indicates that the user mixed real and integer numbers in an expression in such a way that the real number had to be converted to an integer This resulted in the loss of the decimal por tion of the real number The user probably used real division instead of integer division DIV somewhere in the expression I K CANNOT EXCEED N FOR COMB N K AND PERM N K int COMB k n int expression on line linenumber gt This error indicates that an attempt was made to compute the combinations of n things taken more at a time than there were things to take The user probably specified the parameters to the built in function in the wrong sequence Check the expression very carefully to make sure K CANNOT EXCEED N FOR COMB N K AND PERM N K int PERM k n int expression on line linenumber gt This error indicates that an attempt was made to compute the permutations of n things taken more at a time than there were things to take The user probably specified the parameters to the built in function in the wrong sequence Check the expression very carefully to make sure I KEYWORD BOOLEAN MISSING FOR BOOLEAN CONSTANT INPUT OR DEFINITION gt This error indicates tha
142. owed Try asking for less The default is o 100 for workstations and o 50 for the IBM PC GI POSTFIX EXPRESSION STACK OVERFLOW SPECIFY O OPTION COMMAND LINI OPTIONS TOO BIG gt This error is the VMS equivalent of the previous error LH POSTFIX EXPRESSION STACK OVERFLOW SPECIFY O OPTION id This error indicates that a very long expression was being parsed The expression was longer than ever anticipated If the expression cannot be simplified then increase the allowable size with the o num command line option or in a C OPTION O num statement as the first line of the input file The default is o 100 for workstations and 0 50 for the IBM PC POSTFIX EXPRESSION STACK OVERFLOW SPECIFY O OPTION id This error is the VMS equivalent of the previous error PRODUCT OF DIMENSION RANGES IS GREATER THAN 256 id This error indicates that the user declared a doubly subscripted array table with more than 256 total elements in it Try using a smaller table size PROGRAM MUST CONTAIN AT LEAST ONE TRANSITION id I This error indicates that the program did not contain any TRANTO statements Every ASSIST input file must contain at least one transition PROMPT MESSAGE IS TOO LONG MESSAGE TRUNCATED message gt This error indicates that the prompt message specified in an INPUT statement was lo
143. probably missing and that insertion of the missing closing bracket would probably prevent the detection of more extraneous errors The insertion was therefore made but the user will have to fix the problem before the model can be generated MUST REBUILD USING THE HUGE MEMORY MODEL ASSIST gt If ASSIST is compiled for use on a 386 or 387 IBM PC then the huge memory model of the Microsoft C compiler must be used Since SURE will not run on an IBM PC ASSIST is not yet supported on the PC If a user site ports ASSIST to the PC be sure to run the production version of an ASSIST file through a tested SUN or VAX version before accepting the results See your sys tem manager MUST SPECIFY THE WHOLE ARRAY NOT SCALAR ELEMENT gt Certain built in functions operate on all the array elements When this is the case the user may not specify a subscript after the name of the array NAME OF AN ARRAY EXPECTED id gt Certain built in functions operate on expressions or arrays An attempt to pass in an implicit func tion with parameters as if it were an array will cause an error NAMED CONSTANT EXPECTED token BEFORE CONCATENATION OPERATOR gt This error indicates that something other than a named constant was encountered preceding a con catenation character when the syntax for ASSIST requires a named constant The token found instead of the named constant is echoed State
144. problem can be caused when one of the destination expressions is miss ing an operator causing ASSIST to think that the destination clause is finished when in fact it really is not The user should check the expression immediately prior to the designated token for validity REAL DIVIDE BY ZERO real real expression on line linenumber gt This error indicates that during rule generation an illegal attempt was made to divide by zero The user should check the rule section for validity especially in the vicinity of the flagged expression Lines are numbered in the log file REAL EXPRESSION EXPECTED expression on lin linenumber gt This error indicates that during rule generation an expression was evaluated and it resulted in a nonreal value This error is fairly uncommon since ASSIST does a pretty thorough job of finding type mismatches during parsing REAL EXPRESSION EXPECTED token gt This error indicates that during parsing the echoed token was found in a real expression when it does not belong there Usually the token is some kind of a relational operator which would be valid only in Boolean expressions If necessary a Boolean expression can be changed to a numeric expression by counting it with the COUNT function REAL NUMBERS NOT ALLOWED EXCEPT IN RATE EXPRESSIONS func gt This error indicates that a real valued built in func
145. r the transition The syntax for the simple TRANTO statement is given by IF lt condition gt TRANTO dest by rate The condition is a Boolean expression The destination state can be specified as either a state node vector format or as an assignment list list format Mixing of the two specification formats in the same TRANTO is not allowed State space variables may be referenced in any of the three clauses of a TRANTO statement but they can be changed only in the destination clause Integers can appear in all three clauses but only the rate clause can contain real numbers When a transition is processed the source state value for a state space variable is used if its value does not change during the transition For example if NWP and QOO are state space variables and NWP 4 and QQO 22 before the transition then the clause TRANTO NWP QQQ QQQ NWP 21 will set NWP to 5 and QQQ to 22 4 18 in the destination state The source state value of NWP is used to compute QQQ even though NWP has already been incremented in the destination state during the previ ous assignment Condition expression The optional first expression following the IF is the condition expression Condition expressions must be Boolean expressions Conceptually the condition expression determines on which model states to apply this rule For example in SPACE Al 1 5 A2 0 1 IF Al gt 3 AND A2 0 TRANTO the conditional expres
146. rence had fewer parameters passed than were expected Check for consistency between the reference on the line in error and the corresponding IMPLICIT statement TOO FEW CALLING PARAMETERS MORE EXPECTED token gt This error indicates that a built in function reference had fewer parameters passed than were expected Check for consistency between the reference on the line in error and the definition of the built in function being used Section 3 1 8 details the different built in functions TOO FEW SUBSCRIPTS THIS IS A DOUBLY SUBSCRIPTED ARRAY arrayname gt This error indicates that a doubly subscripted array was referenced with fewer than two subscripts Check for consistency with the declaration of the array TOO MANY CALLING PARAMETERS REMAINING IGNORED token FUNCTION func gt This error indicates that the FUNCTION reference had more parameters passed than were expected Check for consistency between the reference on the line in error and the corresponding FUNCTION statement TOO MANY CALLING PARAMETERS REMAINING IGNORED token IMPLICIT impl gt This error indicates that the IMPLICIT reference had more parameters passed than were expected Check for consistency between the reference on the line in error and the corresponding IMPLICIT statement 85 TOO MANY CALLING PARAMETERS REMAINING IGNORED num gt This
147. riad and by adding a flag to signal the dependencies between failed computers the system may be modeled with a much smaller state space When the user combines the resulting complex transition rules by using logical reasoning the system described above can be modeled by the following input file 2 TRIADS OF COMPUTERS WITH 1 TRIAD OF POWER SUPPLIES CONNECTED SO THAT 1 COMPUTER IN EACH TRIAD IS CONNECTED TO EACH POWER SUPPLY THUS IF A POWER SUPPLY FAILS THEN ONE COMPUTER IN EACH RIAD FAILS THE SYSTEM FAILS IF EITHER ey TRIAD OF COMPUTERS FAILS LAM PS 1E 6 Failure rate of power supplies LAM C 1E 5 Failure rate of computers SPACE NFP ARRAY 1 2 OF 0 3 Count of failed computers each triad NFS 0 3 Count of failed power supplies SAME BOOLEAN Set if all failed computers fall on same power supply FUNCTION OTHER II 3 II START 2 OF 0 0 TRUE FOR IX IN 1 2 DEATHIF NFP IX gt 1 IF NFP OTHER IX gt 0 THEN Other triad has a failed computer RANTO NFP IX BY LAM C Failure of computer on same power supply as other failed one RANTO NFP IX SAME FALSE BY 2 NFP IX LAM C Failures of computers on different power supplies than the other failed one x
148. rst form TRIM OFF is for no trimming and is the default The second form TRIM ON selects the trimming bound described in the White Palumbo paper In TRIM ON mode the model is altered so that each state in which the system is experiencing a recovery has all failure transitions from it that do not immediately end in a death state ending in an intermediate trim state There is a transition from the intermediate trim state to a final state at rate Q trimomega For example trim TRIM ON WITH 6e 4 The The WITH clause is optional if it is absent the user will be prompted for a value for value must be entered in response to the prompt and must be terminated with a semicolon trim 28 The third form specifies use of the White Palumbo trimming bound plus the generation of an extra transition from each pruned state to an additional pruned state at the same rate Q The user is again referred to reference 7 to justify trimming TRIM ON or TRIM FULL and to determine if this method is valid for the particular system class To be conservative the lt trimomega gt value should be set as the sum of the failure rates of all system components The justification for the TRIM FULL method is as follows Each pruned state of the model is not a system death state Thus another failure of some component must occur before system failure can occur The TRIM FULL feature simply includes this extra failure transition before pruning th
149. s in parentheses The following example illustrates the definition and invocation of FUNCTIONS FUNCTION F X Y X Y IF 2 F MMM 3 gt 4 THEN In the above example FUNCTION F is declared to be a function of two parameters namely X and Y Its value is computed as the sum of both parameters The reference to the function F X Y would be expanded to form the following IF clause IF 2 MMM 3 gt 4 THEN In this example the expanded form is shown with parentheses around the function operations When the expression is evaluated and the function is expanded the operations within the function will be given precedence and will be performed first A value must be passed for each parameter during invocation so that it can be substituted for the parameter A passed value can be a number a named constant a variable or an expression The function body may not contain any variables that are not listed in the declared parameter list For example if NWP is a state space variable defined in the SPACE statement it cannot appear in the body of the FUNCTION FOR index variables must be listed in the parameter list in order to be refer enced in the body Named constants are allowed in the body of a FUNCTION 12 2 5 VARIABLE Statement The VARIABLE statement is used to define a variable that is not explicitly a state space variable itself but which is dependent upon the state spa
150. s three processors with intermittent fault arrival rates of A r When an intermittent fault arrives it is assumed to be in an active state i e it is actively producing errors After arrival intermittent faults change to a benign state at fast exponential rate D and change to an active state again at fast exponential rate a A solution using STEM or PAWS is necessary because the SURE program cannot handle the fast loops in this model Ck Cckckckckckckckckckckckckckckck ckckckckck ck kk kk KKK KK KK ckckckckckokckckckck ck ck ck ck ck ck kk kk kK aK KER RATE CONSTANTS KKR aK kK KKK KKK KKK KKK KKK KKK KKK ck ck kk kk KKK KK KKK KKK KKK KKK KK KKK ck ck kk ck L_I_triad 0 707e 4 Arrival rate of intermittent fault for triad ALP_triad 2 718281e3 Rate benign triad intermittent goes active BET_triad 3 141592e3 Rate active triad intermittent goes benign KKK KK KK KKK KKK KKK KKK KKK ck kc kk ck KKK KKK KKK KKK KK KKK KK KKK KK KKK KK kk IU SPACE CONSTANTS BRK kk kk KKK KKK KKK KK ck ckckckck ck ckckck ck ck ck kc k kk kCckCkckckckckckckckckckckckckck ck ckckck ck ck ck kc k kk 44 NI_triad SPACE 97 NTOT NI triad W triad FA triad FB triad IMPLICI N IMPLICI IMPLICI START NI triad 0 0 ASSI Ei IF Ha ENDIF BY FAS FA_triad gt RANTO N
151. s warning indicates that a token was missing Since it was obvious what it was it was fixed This serious warning message appears when one or more levels of error reporting are requested I MODEL CONTAINS RECOVERY TRANSITIONS DIRECTLY TO DEATH STATE AND THERE FORE MAY NOT BE SUITED TO TRIMMING id This warning indicates that the user trimmed the model in such a way that the assumptions made when proving the theorem for the trimming bound are no longer valid therefore the user may not be able to trust the answer This serious warning message appears when one or more levels of error reporting are requested F E F zb MODEL CONTAINS RECOVERY TRANSITIONS DIRECTLY TO PRUNE STATE AND THERE FORE MAY NOT BE SUITED TO TRIMMING id This warning indicates that the user trimmed the model in such a way that the assumptions made when proving the theorem for the trimming bound are no longer valid therefore the user may not be able to trust the answer This serious warning message appears when one or more levels of error reporting are requested F P F E NO TRANSITIONS GENERATED USING TRANTO ON LINE linenumber gt This warning indicates that the TRANTO on the specified line was never used This warning may signal a logical error in the ASSIST input file however the need for this TRANTO statement may have been obviated by pr
152. se a space expression can contain a nested space expression Nesting allows for states such as the following 6 0 2 2 2 8 6 0 2 2 4 1 4 TRUE 8 FALSE 4 Only constant expressions may appear in a START statement The statement must not contain any state space VARIABLES or IMPLICITS Some examples of START statements follow START 3 Count of working in triad 0 Count of active failed in triad 07 Count of benign failed in triad 0 Number of component failures for PRUNEIF START 3 OF TRUE Each working in triad NSI_pool Spares count COLD pool pool 20 0 Number of component failures for PRUNEIF These START statements correspond precisely to the respective examples in the SPACE statement section 12 2 7 Rule Section Rules are used to describe the manner in which system components fail and how the system responds to any failures that occur A typical system has a number of different components that fail at different rates Some components may have transient or intermittent faults Some components may be replaced with spares upon failure There may be dependencies between the components All these behaviors are formulated into a set of model generation rules The rule section of the input file begins with the first rule Once the rule section begins definitions are no longer allowed Sever
153. section 3 2 7 1 for more details EN ANGLE BRACKETS IN A THERE MUST BE EXACTLY ONE EXPRESSION FOR A SLOW TRANSITION RATE id This error indicates that an incorrect number of expressions were listed when specifying a slow transition rate in the rate expression for a TRANTO statement If the user meant to give a mean and standard deviation then angle brackets are required If the user meant to have a slow transition rate then an operator is probably missing from the expression or there may be an extraneous comma See section 3 2 7 1 for more details THIS FORM INVALID WITH FAST KEYWORD token gt This error indicates that the user tried to mix the FAST key word with an incompatible form in the transition rate for a TRANTO statement The user probably mixed the FAST key word with White s Method as in BY FAST lt mean sigma gt Use the FAST key word or the angle bracket syntax but not both See section 3 2 7 for more details TOO FEW CALLING PARAMETERS MORE EXPECTED token FUNCTION func This error indicates that the FUNCTION reference had fewer parameters passed than were expected Check for consistency between the reference on the line in error and the corresponding FUNCTION statement OO FEW CALLING PARAMETERS MORE EXPECTED token IMPLICIT impl gt This error indicates that the IMPLICIT refe
154. ser gets this message it is usually because the user has a lot of scratch files in the direc tory Files that are no longer required should be deleted VMS users can use the PURGE command to delete multiple versions of the same file If after cleaning up the error still occurs then the sys tem manager should be contacted to get the user s quota increased EMPTY LIST SPECIFIED id This error indicates that the user followed a left parenthesis by a right parenthesis or a left bracket by a right bracket It could also indicate that an INPUT statement did not specify any constants to be input or that a SPACE statement did not have any state space variables or that a TRANTO did not list any destination expressions The enclosed text may have been commented out as in LE 1 2 ES EOF REACHED BEFORE COMMENT TERMINATED on line nnn gt This error indicates that a comment starting on the specified line was never terminated with a matching EOF REACHED BEFORE COMMENT TERMINATED on line nnn gt This error indicates that a comment starting on the specified line was never terminated with a matching p EOF REACHED BEFORE NESTED RULE SEQUENCE TERMINATED ELSE OR ENDIF MISSING gt This error indicates that no matching ELSE or ENDIF was found for a THEN The user should use the xref option to
155. sfy the parameter requirements as declared in the IMPLICIT NFP line When TOTALF is referenced in the DEATHIF statement no parameters are specified none are expected as was declared inthe IMPLICIT TOTALF line If an IMPLICIT is declared without a parameter list then it must be referenced without one If an IMPLICIT statement is declared with a parameter list values must be passed for all parameters during invocation so that they can be substituted for their respective parameters Passed values can be numbers named constants variables or expressions For example the following log file excerpt shows the incorrect reference of some IMPLICIT functions 0005 SPACE NWP ARRAY 1 5 OF 0 3 0007 IMPLICIT NFP NWP III 3 NWP III 0011 IF NFP 3 TRANTO NWP IX BY 1 2e 3 ERROR TOO FEW CALLING PARAMETERS MORE EXPECTED IMPLICIT NFP 0012 IF NFP IX IX 3 TRANTO NWP IX BY 1 2e 3 ERROR TOO MANY CALLING PARAMETERS REMAINING IGNORE 7 IMPLICIT NFP ERROR SKIPPING EXTRANEOUS TOKENS IX 0013 IF NFP lt 3 TRANTO NWP IX BY 1 2e 3 ERROR LEE EXPECTED lt IMPLICIT NFP One may wish to define an IMPLICIT that is a function of three FOR index vari
156. sion unless it is running on systems where four character extensions are illegal in which case the listing file has the alg file extension Each input line printed in the listing file is numbered for user convenience when the user is making corrections to a line The user should make all corrections to the ASSIST input file ast and not to the listing file The name of the ASSIST input file followed by the date and time of execution is printed in the upper left hand corner of each page of the listing file The page number is printed in the upper right hand corner of each page of the listing file If any errors were encountered while parsing the ASSIST input file they are printed after the input line containing the error the model file is flagged as erroneous and no transitions are generated An attempt to run such a model file through SURE will be rejected If any errors are encountered during model generation the model file is flagged as erroneous An attempt to run such a model file through SURE will be rejected Errors encountered during model generation are printed after the input file list ing and optional variable or load maps The following is a sample log file a3 ast 3 16 94 10 02 49 a m ASSIST 7 1 NASA LaRC Page 1 0001 SPACE A B C D 0002 START 2 OF 3 1 OF 2 1 0003 IF C 2 TRANTO C C 1 BY A B C D 0004 DEATHIF C22 PARSING TIME 0 15 sec RULE GENERATION TIME 0 00 sec
157. sion is true for states 4 0 and 5 0 only This TRANTO rule will therefore only be applied to these two states Note that the key word IF is used to begin two different kinds of statements in the ASSIST lan guage If the condition is followed by the key word TRANTO as in the above syntax the statement is a TRANTO statement If the condition is followed by the key word THEN the statement is a block IF construct and not just a simple TRANTO statement The simple TRANTO statement contains exactly one transition and may not contain any other rules such as FOR DEATHIF statements and so on The block IF can contain any or all of these and will be detailed in section 12 2 7 2 Destination state The vector or assignment list following the TRANTO reserved word defines the transition destination state to be added to the model The destination state can be specified using posi tional or assigned values The assignments define the destination state by specifying the change in one or more state space variables from the source to the destination state There can be as many assignments as there are state space variables The syntax of the TRANTO destination is assignment assignment or lt space expr item gt lt space expr item gt The syntax of the second form is almost identical to that of the START state The only difference is that empty positions are legal for the TRANTO but
158. space variable names are not allowed before a con catenation operator If a state space array element must be referenced in a rate expression use the array syntax with the index in square brackets NEGATIVE VALUES NOT ALLOWED USE A WHOLE NUMBER int COMPUTED gt This error indicates that a negative number was found where a whole number zero or positive was expected Negative integers are not allowed in the rule section except in rate expressions 77 NEGATIVE VALUES NOT ALLOWED USE A WHOLE NUMBER int IS THE COMPUTED VALUE gt This error indicates that a negative number was computed for a constant expression where a whole number is required This error usually indicates that one of the bounds on a state space variable in the SPACE statement is negative or the repetition count to the left of the OF key word ina START statement is negative NEGATIVE VALUES NOT ALLOWED USE A WHOLE NUMBER int COMB n lt 0 expression on line linenumber gt This error indicates that during rule generation a negative number was computed and passed to the built in function COMB The user needs to check the input file for an incorrect specification of the model The expression that caused the problem can be most quickly located by examining the log file NEGATIVE VALUES NOT ALLOWED USE A WHOLE NUMBER i
159. st precede all other commands including any other debug commands For example the statement C OPTION LEL 10 in the input file is the same as the following command line options lel 10 Adi The following options are available e c Specifies identifier case sensitivity Use of c is not recommended since SURE is never case sensitive Case sensitive state space variables are safe to use because they are never passed to SURE Case sensitive constant names will cause problems because they are passed to SURE The default is not having case sensitive identifier names e pipe This option causes the model output to be written to standard output instead of to a model file and is useful if one wishes to pipe the model directly to SURE This option is valid only under UNIX An attempt to use it under VMS will cause ASSIST to print an error message The default is no rerouting of the model file to the standard output file e map This option causes ASSIST to produce a cross reference map of all the definitions of and references to identifiers and literal values in the program The map also tells which ENDFOR matches which FOR and which ENDIF matches which IF Italso indicates to which IF an ELSE belong Although the map is several pages long it may help the user find misspelled identifiers Use of the map is recommended during the first few executions of a new input file The default is no cross reference map
160. stems that could be modeled independently However as flight critical systems become more complex and more highly integrated the Markov models describing them will become enormously complex The complexity of the model stems from the interactions between failure and recovery processes of the various subsystems which can no longer be modeled independently Often even the most complex system characteristics can be described by relatively simple rules The models only become complex because these few rules combine many times to form models with large numbers of states and transitions between them The rules describing the behavior of each sub system can be developed and verified separately the submodels are then easily combined to accurately model the behavior of the entire integrated system Butler ref 3 developed an abstract high level lan guage for describing system behavior rules and a methodology for automatically generating semi Markov models from the language This methodology was implemented in a computer program the Abstract Semi Markov Specification Interface to the SURE Tool ASSIST ASSIST is written in ANSI standard C and executes under the VMS and UNIX operating systems The ASSIST program produces a file containing the generated semi Markov model in the format needed for input to the Langley developed reliability analysis programs SURE STEM Scaled Taylor Exponential Matrix and PAWS Pad Approximation with Scaling ref 4
161. stics such as the number of failed processors or the num ber of spares The model generation rules are first applied to a start state The rules create transitions from the start state to new states The program then applies the rules to the newly created states This process is continued until all states are either death states or have already been processed The expres siveness of the ASSIST language is derived from the use of recursive semantics for its constructs Thus a small compact description in the ASSIST input language can efficiently yet accurately represent the failure behavior of a system that may require an extremely large semi Markov model to solve for system failure probability Absorbing model states i e states with no transitions leaving them represent system failure Typ ically the reliability engineer needs to determine the probability of entering an absorbing state within the specified mission time The absorbing state death conditions of the model must be defined in terms of state space variables These death conditions could be system failure the onset of degraded perfor mance operation or other situations resulting from failures Consider an example system that has a triad of processors performing the same function A majority voter is used to detect and resolve any discrepancies between the outputs of the three processors A semi Markov reliability model for this example appears in figure 6 In this figure the tria
162. t expression on line linenumber gt This error indicates that during rule generation the user tried to divide by zero in order to obtain the cyclically wrapped integer remainder This is illegal do not do it INTEGER DIVIDE BY ZERO int DIV 0 expression on line linenumber gt This error indicates that during rule generation the user tried to divide by zero in order to obtain the integer quotient This is illegal do not do it INTEGER EXPRESSION EXPECTED expression on line linenumber gt This error indicates that during rule generation an expression that must evaluate to an integer evaluated to a real or Boolean This error is fairly uncommon since ASSIST does a pretty thorough job of finding type mismatches during parsing INTEGER EXPRESSION EXPECTED MOD CYC DIV gt This error indicates that during rule generation an expression that must evaluate to an integer evaluated to a real or Boolean This error is fairly uncommon since ASSIST does a pretty thorough job of finding type mismatches during parsing INTEGER EXPRESSION EXPECTED token gt This error indicates that during parsing an expression that must evaluate to an integer evaluated to a real or Boolean It can also indicate that a strange token was found where an integer expres sion was expected INTEGER EXPRESSION EXPECTED gt This error indicates that during
163. t char non quote ascii lt space expr li 59 lt space expression gt BY input list named constant lt named constant gt prompt message lt named constant gt lt function parm list gt index parm list lt impl parm list gt quot text char st gt lt space expr list gt lt space expr item gt lt space picture gt space item list space item lt space expr item gt lt space expr item gt lt space expr list gt whole or boolean lt whole expression gt expression gt lt space expression gt xpression gt OF lt whole or boolean lt space item list gt lt space item gt lt space item gt lt space item list gt lt state space var gt lt state space var gt lt i range gt state space var BOOLEAN lt space picture gt state space var ARRAY lt array range gt state space var ARRAY array range OF lt i range gt lt state space var gt ARRAY array range OF BOOLEAN array range space destination list lt space destination gt lt i range gt lt i range gt lt i range gt space destination lt space destination gt space destination list dest adj clause dest adj clause lt state space var gt whole or boolean expression lt state space var gt inc op lt for range gt lt set
164. t defines 4 3 4 4 4 5 2 3 and 3 3 as pruned states e Like the death states the generated pruned states are lumped together according to the PRUNEIF statement they satisfy Thus the contribution to system failure caused by pruning can be determined easily from examining the SURE output The pruned states are always lumped regardless of the setting of the ONEDEATH option In a model that is generated from an input file with three DEATHIF state ments and two PRUNEIF statements states 1 through 3 will be death states corresponding to the three DEATHIF statements and states 4 and 5 will be pruned states corresponding to the two PRUNEIF statements The specific algorithm used to assign state numbers is detailed in section 4 3 The ASSIST program generates a statement in the model file that identifies the pruned states in the model For example the model with three death states and two pruned states would contain the statement PRUNESTATES 4 5 The SURE program will use this statement to list the pruned state probabilities separately from the death state probabilities Note Versions of SURE earlier than 6 0 will simply list the pruned states as if they were death states PRUNEIF statements may be included inside FOR and block IF constructs but they may not be included within TRANTO statements These features are described in the next few s
165. t file contains binary numeric data tables and pseudo machine code This file is currently used as a temporary file however future versions of ASSIST may make additional use of it The object file has the aobj file extension unless it is running on systems where four character extensions are illegal in which case it has the aoj file extension 15 1 4 Temporary Files The ASSIST program language uses several temporary files to process the ASSIST INPUT state ments and to store variable definitions for the optional cross reference map which is listed on the log file Temporary files are deleted automatically after successful generation of the model file Tempo rary file names are system dependent They begin with QQ and end with a sequence of digits Tempo rary file names usually do not contain an extension 16 Examples In this section the use of ASSIST to generate semi Markov models will be illustrated by several examples 16 1 Triad With Cold Spares This sample architecture has a triad of processors in which all three processors execute the same program In addition to the triad the sample architecture contains a pool of two cold spare processors Each processor receives identical inputs so that all nonfaulty processors produce the same output The three outputs are voted and any incorrect outputs are masked by the voting as long as a majority of the active processors are nonfaulty A faulty processor is detected by the voter and
166. t of an array evalu ated to a value that was not within the declared range For example if the array is bounded 5 11 and referenced with an expression evaluating to 12 then this error will occur The user should check the expression for mistakes or increase the range of the array ARRAY DIMENSION S MISSING token gt This error indicates that the key word ARRAY was used but no subscript bounds were given inside brackets The user may have forgotten the brackets entirely or may have used brackets but omitted an expression between them The error could also be caused by an extraneous comma ARRAY SUBSCRIPTS MUST BE ENCLOSED IN id gt This error indicates that an array subscript was given but no square brackets were found This error usually occurs when an array is referenced with parentheses instead of square brackets The user should change the to 66 ATTEMPT TO DEFINE RECURSIVE FUNCTION IMPLICIT DISALLOWED num gt This error indicates that a FUNCTION or IMPLICIT made reference to itself For example FUNCTION FOO X FOO 12 X is illegal because the function FOO references itself by computing FOO 12 in the body of the function definition The user should rethink the problem and change the function body ATTEMPT TO TAKE LN OF NEGATIVE NUMBER expression on line line number gt This error indicates that during rule generation an illegal attempt
167. t the expression pointed to evaluated to a Boolean value when a numeric expression was expected in an INPUT or constant definition statement The user must tell ASSIST if a Boolean constant is being defined For example FLAG BOOLEAN X gt Y KEYWORD IN IS MISSING id This error indicates that the FOR statement requires the word IN before the set defining the FOR range The user must say something like FOR III IN 1 10 75 KEYWORD OR SEMICOLON EXPECTED id gt This error indicates that something other than a key word or semicolon was encountered when the syntax for ASSIST requires a key word or semicolon The token found instead of the key word or semicolon is echoed There might be some extraneous text at the end of a DEBUGS C_OPTION or option definition statement KEYWORD USED IN WRONG CONTEXT DID YOU MEAN TO SAY IMPLICIT gt This error indicates that the user used a reserved word in the wrong place The user probably said INTRINSIC instead of IMPLICIT KEYWORD USED IN WRONG CONTEXT WITH CLAUSE INVALID WHEN TRIM OFF gt This error indicates that the user used the reserved word WITH in the wrong context The user probably tried to specify a value for Q im when trimming was off See section 4 2 for more details on trimming KEYWORD USED IN WRONG CONTEXT id This error indi
168. t yet supported At release 7 0 of ASSIST there are no features that generate this error NUMBER OF ELEMENTS DOES NOT MATCH NUMBER OF ELEMENTS IN PREVIOUS ROW OF DOUBLY SUBSCRIPTED ARRAY CONSTANT id This error indicates that a doubly subscripted array constant is being declared but the rows of the table do not all have the same number of elements If the rows are supposed to have different lengths then pad the shorter rows with trailing zeros so that all rows have the same length NUMBER OF ERRORS EXCEEDS LIMIT OF 40 This error indicates that the maximum number of errors per input file has been exceeded ASSIST will therefore no longer continue parsing the input file for additional errors warnings The limit can be increased with the el command line option as in elz50 The errors will ultimately have to be fixed anyway so it is good practice to start correcting them even if the limit is being increased I NUMBER OF ERRORS LINE EXCEEDS LIMIT OF 3 gt This error indicates that the maximum number of errors per line has been exceeded ASSIST will therefore no longer continue parsing the input file for additional errors warnings The limit can be 78 increased with the lel command line option as in lel 10 The errors will ultimately have to be fixed anyway so it is good practice to start correcting them even if
169. the allowable size with 71 the o num command line option or in a C OPTION O num statement as the first line of the input file The default is o 100 for workstations and o 50 for the IBM PC INFIX EXPRESSION LIST OVERFLOW SPECIFY O OPTION id This error is the VMS equivalent of the previous error INSUFFICIENT MEMORY FOR PARSE PHASE gt This error indicates that the ASSIST input file is too big to parse Since ASSIST will typically parse programs bigger than it can solve it will probably be necessary to rethink the problem and make it simpler INSUFFICIENT MEMORY FOR PARSE PHASE bytes BYTES OPERATING SYSTEM MALLOC LIMIT num gt This error indicates that the total table size was bigger than ASSIST will allocate The error always arises from large values for the b e o i n p nest pic and rule options Try decreasing the value specified on the command line for one or more of these options The default is pic 100 for workstations and pic 100 for the IBM PC The default is i 400 for work stations and i 200 for the IBM PC The default is n2200 for workstations and n 50 for the IBM PC The default is 02100 for workstations and 0250 for the IBM PC The default is nest 16 for workstations and nest 8 for the IBM PC The default is n2200 for work stations and n 50 for the IBM PC The default is b 1024 for workstations and b225
170. the expression evaluates to an integer then the constant will be an integer constant If the expression evaluates to a real number the constant will be a real constant If one of the values in the expression is an integer but con tains a decimal point the constant will be a real constant even though its value might be an integer The user must use the word BOOLEAN to specify that the constant will be a Boolean constant For example FLAG BOOLEAN NP gt 3 Optional parentheses may be added for clarity FLAG BOOLEAN NP gt 3 The complete syntax of a constant definition is lt identifier gt BOOLEAN lt definition clause gt where lt definition clause gt defines either a scalar or an array Its syntax is lt expr gt or lt gt oF Bape 5 lt gt oF lt expr gt hi or ARRAY lt gt OF lt expr gt it OF lt expr gt 10 The third form is included for compatibility with prior versions Doubly subscripted arrays are also allowed via repetition of the second form listed above The syntax is lt gt OF expr lt gt OF lt expr gt Li so oF ec 45 oF x Y1 All nonBoolean constants are echoed to the model output file An ASSIST identifier must not exceed 28 characters Identifiers used for named constants that will be passed to SURE must be unique in the first 12 characters Constant array names should not exceed 8 char
171. they can be 94 written to the model file the same way they were typed into the input file The default is a maxi mum of 200 unique numerical values in the table for most systems 50 on the IBM PC o nnn Specifies the maximum number of operands that can be held in the expression operand list while parsing a single statement The default is 300 on most systems 50 on the IBM PC The maximum number of infix postfix operations is a function of this number and is always signifi cantly greater e nnn Specifies the maximum number of expressions that can be held while parsing a single statement The default is 300 on most systems 50 on the IBM PC p nnn Specifies the maximum number of identifiers for a FUNCTION or IMPLICIT or VARIABLE parameter list The default is 64 on most systems 32 on the IBM PC b nnn Specifies the maximum number of tokens in the body per FUNCTION IMPLICIT or VARIABLE definition The default is 1024 on most systems 256 on the IBM PC w nnn Specifies the levels of warnings that will be issued The higher the number the more warnings Levels available are 0 for no warnings through 99 for all warnings There are cur rently only three levels defined The default is two levels of warning reporting The W FEWER form decreases the level to one less level of warnings The W NONE form suppresses all warnings The W ALL form enables all warnings 95 References 1 Wh
172. tion and the error will disappear The setup start and rule sections are described in sections 3 2 1 3 2 2 and 3 2 7 respectively They are listed in the BNF description in appendix B SUBSCRIPT NOT ALLOWED ON SCALAR id This error indicates that the identifier in question is being referenced as if it were an array even though it was not declared to be an array Square brackets must be used to declare arrays See sec tion 3 1 5 for details on how to declare constant arrays See section 3 2 1 for details on how to declare state space variable arrays 84 THE REPETITION COUNT PRECEDING THIS OF IS TOO LARGE int REPETITIONS IGNORED gt This error indicates that the repetition count before an OF clause is too large It is probably either a typographical error or an erroneous expression THEN OR TRANTO CLAUSE MISSING FOR THIS IF id gt This error indicates that an IF statement contained neither the THEN nor TRANTO key word There are only two kinds of statements that begin with the key word IF namely the block IF and TRANTO statements See sections 12 2 7 1 and 12 2 7 2 for details LT THERE MUST BE EITHER TWO OR THREE EXPRESSIONS BETWI RATE EXPRESSION id This error indicates that an incorrect number of expressions were listed when using White s Method to specify the transition rate expression in a TRANTO statement See
173. tion such as GAM was found somewhere other than in a rate expression or constant definition REAL NUMBERS NOT ALLOWED EXCEPT IN RATE EXPRESSIONS id gt This error indicates that a real number was found somewhere other than in a rate expression or constant definition REAL VALUE EXPECTED gt This error indicates that the resulting type of an expression was not a real number The token at the end of the erroneous expression is echoed RELATIONAL OPERATOR MUST FOLLOW NUMERIC QUANTITY IN BOOLEAN EXPRESSION id gt This error indicates that when parsing a Boolean expression a numeric expression came to an end but was not followed by a relational operator to compare it with some other numeric quantity The user should fix the expression and rerun RELATIONAL OPERATOR NOT ALLOWED IN A NUMERIC EXPRESSION id gt This error indicates that when parsing a numeric expression a relational operator was encoun tered The user should fix the expression and rerun RIGHT EXPECTED func REQUIRES 1 num PARAMETERS AND NO MORE gt This error indicates that something other than a right parenthesis was encountered in the parameter list for a built in function when the syntax for ASSIST requires a right parenthesis The token found instead of the right parenthesis is echoed This error usually occurs when more parameters are passed to a built in fun
174. to compute the natural loga rithm of a negative or zero number was made The user should examine the log file to check the expression for mistakes and check the ASSIST input file rule section for correctness ATTEMPT TO TAKE LN OF NEGATIVE NUMBER real lt 0 000000000 expression on line linenumber gt This error indicates that during rule generation an illegal attempt to compute the natural loga rithm of a negative or zero number was made The user should examine the log file to check the expression for mistakes and check the ASSIST input file rule section for correctness ATTEMPT TO TAKE SQRT OF NEGATIVE NUMBER real lt 0 0000000000 expression on line linenumber gt This error indicates that during rule generation an illegal attempt to compute the square root of a negative or zero number was made The user should examine the log file to check the expression for mistakes and check the ASSIST input file rule section for correctness ATTEMPT TO TAKE TAN AT SINGULAR POINT PI 2 3 PI 2 ETC expression on line linenumber gt This error indicates that during rule generation an illegal attempt was made to take the tangent of ma 3 22 expression for mistakes and check the ASSIST input file rule section for correctness a number near a singular point such as The user should examine the log file to check the BAD TYPE IN A NUMERIC EXPRESSION id gt
175. torte tac a toa e TP ER ERU t gue dea ere e p eco Ee ee bys 21 32 3 T LRANTO statement tec 3 eL EAE OC Eee a e US 21 3 2 12 Block IE constr ct ea Doce t te Nc AU T e RR bea ER ese Do ed dte 24 3 21 13 FOR GORSLUCLU ua oom rn de o s e e oet teen e poen uic ea or a s 24 IATA ASSERT statement seg 54d prd d RN e dod eee abes 26 3327 3 DEACDHIE Statement soi ewe Bru te pibe e Ce Yo e Gen e Rec E ed 26 3 2 7 6 PRUNEIF statement eese RR RR RR Rs 26 4 Model Reduction Techniques 0 0 ccc hr 27 4 1 Model Pruning 4 2 ste obo tuse wea do e dte tesa wes baie eke by adt 28 4 2 Model Trimming eoe iue b RR Syed ein ES hee he ee ERE SEIS A 28 4 3 Assignment of State Numbers 0 0 cee eee eee een teen ens 29 5 Model Generation Algorithm 0 0 0 coke ccc cece cee ene eens 29 6 Fil Processin 3s sak eee eG Ba eek es Wie S er ee Se ee E E Ede 31 6 1 Inp t EMe ooo Se dese sa ae Re PP oda BR eae tare Sade Ula tenu do yaar ane 32 6L T ModelEiless 5 ram deo 1 A ee MyM Met cee My ede AS de ISS aS Wie tte Ai M 32 6 12 Los File ic RR ees EES SRM RENE RES BL ee E 33 iii 6 1 3 Object File asic tater areca Mass oE Steere acne te du Eo te cetera 34 6 14 Temporary Pilesic 366 165 gie oett unie oerte deut d esce aec aei uta 34 T Exampl s 2 ota nearness added vM Ege eae eh cela eda deste esee tubos 34 Vile Triad With Cold Spares sl ner baker iad aroha ed a teen bow iue eee bach 34 7 2
176. ule 4096 for workstations and rule 1024 for the IBM PC INSUFFICIENT MEMORY FOR PARSE PHASE parse library storage func body gt This error is similar to the above error and arises from a large value for the b The default is bz1024 for workstations and bz256 for the IBM PC INSUFFICIEN EMORY FOR PARSE PHASE parse library storage gt This error is similar to the astparse storage error above INSUFFICIEN EMORY FOR RULE GENERATION PHASE allstorage gt This error is similar to the astparse storage error above INSUFFICIEN EMORY FOR RULE GENERATION PHASE data_ptr gt This error is similar to the above error Try pruning or trimming the model 72 INSUFFICIENT MEMORY FOR RULE GENERATION PHASE init_hash_function gt This error is similar to the above error The user probably asked for too large a number of hash buckets with the bc option or too wide a bucket width with the bw option The defaults are bc 1009 and bw 5 INSUFFICIENT MEMORY FOR RULE GENERATION PHASE link to a brand new bucket This error is similar to the above error ASSIST was attempting to obtain more memory for a new state on the ready set but no more memory was available Try pruning or trimming the model FIJ INTEGER CYCLIC WRAP MODULO ZERO int CYC in
177. uning If so the message can probably be ignored but the user should check the input file first to make sure that everything is correct This warning message appears when two or more levels of error reporting are requested NO TRANSITIONS OUT OF A NON DEATHIF STATE THIS STATE IS THEREFORE IMPLICITLY A DEATH STATE statenumber gt This warning indicates that the state statenumber did not have any transitions leaving it yet it did not conform to any of the DEATHIF or PRUNEIF conditions Because there are no transitions leaving it SURE will assume this state is a death state This serious warning message appears when one or more levels of error reporting are requested NOT YET IMPLEMENTED gt This warning indicates that the user tried to use a future option of a pending version of ASSIST that is nearing completion but still under development and not yet supported At release of ASSIST 7 0 there are no features that generate this warning This serious warning message appears when one or more levels of error reporting are requested NUMBER SHOULD BEGIN WITH DIGIT NOT DECIMAL POINT gt This warning indicates that the user began a number with a decimal point There is currently no place in the ASSIST language where this would be ambiguous so this warning never appears unless the user requests all warnings If the syntax ever changes so as to cause th
178. ust be listed in the state space vari able list The optional lt parameter list gt is used to declare an IMPLICIT that is also a function of specified parameters All parameters are positional and must therefore be passed in a consistent order The user decides how many parameters a certain function will have The user may not vary the number of parameters that are passed from the number of parameters that are defined The parameter names in the parameter list are separated by commas Parameter names may be reused in other IMPLICIT or FUNCTION definitions or as FOR indices but they cannot be named constants or state space variable names Any variables such as FOR index variables which are referenced in the body of an IMPLICIT and not already listed as state space variables must be listed in the optional parameter list The body of the IMPLICIT definition is the expression defining the value as a function of the specified state space variables and parameters Named constants and reserved words may be freely ref erenced in the body and must not be specified with either the state space variables or parameters The IMPLICIT may be invoked in TRANTO DEATHIF PRUNEIF ASSERT IF or FOR state ments or in later IMPLICIT or FUNCTION definitions by giving the name followed by the values in parentheses for each of its parameters If the IMPLICIT definition does not include a
179. ut file Quoted SURE statements may also be placed anywhere in the input file Because SURE statements can appear in more than one section they will be described next under the setup sec tion description 12 2 1 Setup Section The Setup Section is first in the ASSIST input file and contains definitions and a terminating SPACE statement The definitions can occur in any sequence except that an identifier may not be refer enced before it is defined The following sections detail the ASSIST statements that are valid in the setup section of the file 12 2 1 1 Constant definition statement A constant definition statement equates an identifier to the value it represents For example NP 3 LAMBDA 0 0052 RECOVER 0 005 These constants are also called named constants to distinguish them from literal values The word constant is used generally to include both named constants and literal values In the above example the name LAMBDA is a named constant whereas the value 0 0052 is a literal value Constants can also be defined in terms of previously defined constants as illustrated LAMBDA 1E 4 GAMMA 10 LAMBDA Once defined a named constant identifier may be used instead of the value it represents Constant definitions remain static throughout the execution thus once a constant is defined it cannot be rede fined to another value The ASSIST language assumes that all named constants are numeric constants If
180. whole expression named constant lt whole expression gt lt state space var gt lt whole expression gt state space var lt whole expression gt 15 lt real expression gt lt whole expression gt lt boolean expression gt lt whole expression gt lt boolean expression gt lt integer expression gt lt numeric expression gt numeric expression bool term expr lt bool term gt lt bool term expr gt or op lt bool term gt bool factor lt bool term gt lt and op gt bool factor lt bool item gt lt bool item gt lt bool item gt lt numeric comparison gt lt simple bool item gt lt whole expression gt lt relation gt lt whole expression gt non index single item truth value boolean function invocation 61 or op lt and op gt lt relation gt inequality relation equality relation numeric expression term expr term factor numeric item Xbin numeric item lt add op gt mpy op lt pow op gt lt sign op gt lt boolean expression gt NOT lt simple bool item gt OR XOR AND amp lt inequality relation gt lt equality relation gt AME NUM lt term expr gt lt term gt lt term expr gt lt add op gt lt term gt lt factor gt lt term gt lt mpy op gt lt factor gt num

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