"user manual"
Contents
1. afl 4 Launching 1 3 6942 EIMA i TT Lanc Ok Initialisation qa E 7 1 2 1942 1 9 079 Step Ex Reconfiguration 1 i B5 TT Reconf 1 51942 umm 1 9 079 Simulation eee 1 5 1942 EE ER HI Anticipation 1 9 079 TT Antic Degraded t Launcher reliability Lifespan Sat reliability 10 gears Nb sat Ist launching Launching decision Nb sat following launching Nb sat launcher Reservation launcher Waiting for launcher Satellite manufacturing Manufacturing decision In orbit reconfiguration Nb Sat Manufactured Nb sat nominal mission Reconfiguration decision Nb sat minimal mission Waiting for reconfiguration Spare on ground Launcher cost Nb Sat Op at Tj Recurring satellite cost Nominal availability at Tj Interest rate Degraded availability at Tj Operational maintenance duration Nb sat Op from Tmin to Tj lt Tmaz Nominal availability from Tmin to Tj lt Tmaz Degraded availability from Tmin to Tj Tmaz j Degraded 8 Satellites Cost from Tmin to Tj lt Tmaz Tmin air years Tmaz rep years Average Min Mas Curve 21 points a HN DJ Nb Sat Op 7 384727 0 29526 7 33616 7 43329 Beginning 0 years Nominal 0 424534 0 05735 0 4251 0 44397 Step years Degraded 0 525318 0 06043 0 61538 0 63526 Cost 2525 179 495 2495 49 2554 51 From Timin o Fines Confidence rate 90 34 3 6 2 Simulator of system architecture This tool can au2. Reliability assessment This example shows how redundancy equipment reliability may be assessed simply by simulation 4 What is the impact of a servicing time following a breakdown Bi Es On satellite optical instrument destruction by solar dazzle T ta xl Teta Yl T ta 70 Initial attitudes sun AD v Y f D Initial speeds Optical instrument cane Delay before destruction Mean value Standard deviation 263 540 33 100 138 207 e 153 0 663 0 326 10 10 00 8 15 3 02 hours degree 64 degree E degree FIN degree second degree second degree second degree C Destruction before satellite ground control Delay 10 heures 33 This example shows how the impact of a post failure servicing time allowance upon equipment destruction probability can be evaluated risk of destructive solar dazzle of an optical instrument mounted on a satellite which is no longer momentarily controlled Ey FX Sim 8 Satellites Launching date Launch 1 35 35 45 45 F025 T0925 85 8B 15 Launch 10 11 5 Launch 1t 14 092 Launch 12 14 032 Launch 13 16 092 Launch 14 16 092 Life duration E Reliability at 5 gears Date of Loss Loss i 85 Success of Availability Launching date Avail t 3 5 Avail 2 3 5 Avail 3 45 uai 4 45 Avail 5 7 09 Avail E 716 Avail 7 3 5 Avail 8 3 5 Avail 8 115 Avail i 12 2 Avail T 14 1 Avai
3. 0 03208563 0 16150198 0 00520505 0 13728862 1 1 teh M Se 20000 40000 60000 80000 100000 Result o 03208563 1s 0 01701181 D 02678368 0 04076908 Number of sales 0 16150198 0 01701181 1 0 0601962 0 70679341 Price 0 00520505 0 02678368 0 0601962 55033147 Resut 0 13728862 0 04076908 0 706798341 0 55033147 2d 3 5 2 Meaning of Processing Operations An online help accessible through buttons E allows to remind user of the meaning of his various options Average Enters the average value of simulation results arithmetical average Standard Deviation Standard deviation is a scattering measurement of values from a population with respect to their average value square root of variance Enters standard deviation of simulation results in population position or Enters standard deviation of a population assessed from simulation results considered as a sample of this population in sample position Variance Variance is the arithmetical average of squares of deviations between values of a population and their average value Enters variance of simulation results in population position or Enters variance of a population assessed from simulation results considered as a sample of this population in sample position Median Enters median of simulation results value splitting in two halves the series of results ordered Kurtosis Enters Kurtosis or coeff
4. Prediction of a selling price of a product sold at auction 45 Normal Law Normal law represents many natural phenomena featured by a variable likely to deviate symmetrically with respect to an average value with a decreasing probability So the standard deviation corresponds to the average of deviations Example deviation between size of parts achieved and predicted size Pareto Law The Pareto Law is a power law defined by 2 parameters the Pareto index K and the minimum value of the variable Very used in quality management it helps to describe a factor more or less decisive 20 of problems generate 80 of the costs Pearson Law The Pearson law or Khi two law is a continuous law the random variable of which is the sum of squares of nu normal reduced independent variables This law is especially used for confidence interval calculations Personalized Law Kaplan Meyer This functionality allows to define any type of statistics law from its distribution function defined on processing sheet Defined by a 2 column matrix values and growing probabilities from O to 1 this function may be entered by user or generated directly by software from experimental data by the Kaplan Meyer method Poisson Law The Poisson law represents the number of occurrences per unit of time of independent events the rate of which is constant probability of occurrence per unit of time Example Number of telephone calls transiting
5. So in example below formula of result of product X may be easily entered in active cell using software proposed dialog box by selecting names in scrolling list TT A 1 8 c D E 1 Launching of the product X Launching cost I404 04054 Price 3r bz44 7 09 Number af sales 1820 468919 Cost per unit 20 30b0b36 Result of X 1291 2 Bbbl USE HAHE EES Mame used Average Result Average Result of X Launching cost Number of sales Selected cell formula Ca Number of sales iPrice Cask per unibj E Launching cast i Select names in list For re copying Ehem in Formula OK Cancel ETT ER e er en e o ert n SS Seeks I I tal ra epi emer epe I eaoicn ts co nr2 cO REx Sim 1 Formula Number of units sold selling price Cost per unit Launching Cost Remark entering operators and parentheses requires to be preliminarily placed in dialog box s box by using mouse 22 3 4 Executing Simulation Command Execute of menu Simulation allows to display dialog box below EXECUTE Number of simulations Selecting parameters Cost_per_unit Launching_cost Number of sales Graph 2 Frequency graph Probability graph Distribution function 3 Distribution function 1 Group up parameters on a similar graph Probability between Vmin and Vmax 0 Confidence interval in 60 Quantle Inf 19 Sup Confidence Wilks 72
6. by simply using computer mouse Such series should be preliminarily entered in line or column on a calculation sheet but not necessarily the one being selected 18 SETTING TO A STATISTICAL LAW This functionality helps you determine the parameters of statistical law selected so that it represents at best experimental data you have Specify address of experimental data in the followina box 5655 6 27 Specify address of censored data in the following box srs5 sts16 7 You may to do so directly select relevant cells Experimental data 3443550423 571 3762946 210 8874544 469 9276715 879 9572749 233 5919596 205 3211566 489 174775 195 507559 321 2724427 466 020545 489 0003397 247 0499503 283 8035958 435 9533378 297 6379249 5572609432 585 9276246 385 1686033 947 9888724 632 8132873 186 7347358 619 2762701 Censored data 1326 03143 843431204 1176 89925 574 960181 550 060086 173 143081 944 564101 115 157476 1310 06107 386 935029 1326 77938 452 392069 From all values of series setting is achieved by software using maximum likeliness method optimization achieved using Simplex method At completion of such setting software displays the experimental distribution function and function of law obtained together with statistical test results Khi 2 Kolmogorov Smirnov enabling user to validate law s selection SET beta 0 8691 Sigma 553 5379 Gamma 186 7347 Khi 2 0 839 Kolmogo
7. cells and press block capital and CTRL keys by entering the function Used in matrix form MARK SIM function helps displaying time T probability Pr to be in the combination of states defined by vector STATE or probabilities P1 to Pn if vector STATE is not defined It gives such results for intermediate time values between O and T if range of selected cells includes various lines Following examples specify the formalism adopted for such function when used in matrix form 38 a Vector STATE is defined 2 columns or more 1 column P 0 82142808 0 78539121 0 76749154 100 0 82142808 r 200 0 78539121 300 076749154 b Vector STATE is not defined column 2 columns P1 P1 P2 0 08 08 J J0l 75790422 13709395 14332265 15914719 C 0 75790422 0 74332265 T 0 73803747 T Nblines 1 0 73803747 17235284 n columns 0 T Nblines 1 P1 P2 Pn os oi J D 15914719 0 04206856 17235284 0 02945406 cc T n columns 1 or more Pn P2 01 i o J 5 Temps P1 100 0 75790422 1370939 06352386 0 04147797 200 1 0 74332265 15914719 0 04206856 0 0554616 300 0 73803747 0 17235284 0 02945406 0 06015563 0 T Nblines 1 O T 39 4 Applications and Joint Application Possibilities Examples shown here are provided for demonstration in online help Some of them illustrate the
8. joint application possibilities between SIMCAB and the other CAB INNOVATION softwares either for controlling scattering in assessments performed by SIMCAB 4 operation safety software or for achieving optimizations using GENCAB software from simulation results 4 1 Controlling uncertainties The following examples show in simple cases how dimensioning problems may be solved by the program in such highly different fields as marketing electronics or mechanics E lei ks Launching of a new product Launching cost 387259875 i M babe Max Price LU GUI 45 77 36 9429184 3 3 E Number of sales 1725 0632 o AM BE ANM Cost per unit 2559116518 1 25 Standard deviation 3 Result 15157 033 Mean result 25112 Standard deviation lt i Graph Iof xi Risk of loss 1 2 Probability graph Mean value 26112 Standard deviation 18858 Probability result 0 1 23 0 16 0 12 i e UU Ifi 0 L i s s gj s S s s FESS What result can we expect from a new product This first example shows immediately the relevance even for highly mere computations to obtain results in distribution form and not in selective assessment form eu ioj x Worst case analysis Voltage V1 27 7080484 v1 R sistor1 19 1015932 R sistor2 8 3396704 R1 Voltage V2 8 4207182 Volts v2 Mean value is Standard deviation 8 55 Probability V2 lt 4 Volts 0 08 How to validate
9. of success and 1 p of failure Example number of failing parts in one production batch Erlang Law The simple Erlang law represents the duration prior to occurrence of a kth Poissonnian type event Example Time before a stock runs out Exponential Law Exponential law represents duration prior to occurrence of an event whose probability of occurrence per unit of time is constant rate Example Time of equipment proper operation with constant failure rate electronic equipment not undergoing wear Gamma Law This is a very general law with two parameters If Beta 1 law is exponential If Beta is an integer K law is the Erlang law If Lambda and Beta Nu 2 with Nu being an integer law is the Ki two law with Nu degrees of liberty Example Time before a stock runs out Geometrical Law Geometrical law represents the number of tests until first success occurs each test being independent with a probability p of success Example number of parts to be achieved before obtaining a proper one Hypergeometric Law Close to the Binomial law the Hypergeometric law represents the number of successes obtained after n print runs without any discount Example number of faulty parts in one sample deriving from a batch of which the initial percentage of elements to be discarded is known Lognormal Law The Lognormal law features a distribution of which the variable logarithm follows a normal law Example
10. simulated Both parameters should be preliminarily selected in both scrolling lists 20 3 6 Treatment of the dynamic systems 3 6 1 Recursive Modelling a Principle Recursive modelling does not describe the behaviour of a system during all its mission but only between two current moments t and tj which corresponds to random state changes of the system failure or repair for example or to the crossing of characteristic thresholds by continuous variables in the case of hybrid systems a mechanism of control activated when a parameter enters in zone of alarm for example It results a simplified simulation exclusively based on logical or calculation operators Classical model a to t t t tj t At mission Each simulation carried out by the tool consists in recopying a certain number of times during all the mission the Ej state defined in cells of the spreadsheet in Ei state defined in the same manner in other cells from an initial state EO defined in addition like illustrates it the following figure At min T t mission j ul The increment At considered by the tool is the smallest computed value among various increments of times Tk defined in another cells of the spreadsheet These times Tk are recalculated at each transition in the Markov case or calculated once and then decremented until they are taken into account otherwise Simulation can be carried out in step by step to validate the models
11. 0 surface under the curve The function of distribution corresponds to the probability that the random variable X is lower than a value X Probability Discrete Probability Continuous 1 F xi X P X xi 0 OO 0 Demonstration pulling of dice and measurement of the size of individuals 100 values Graph of probability Density of probability 0 3 o 0 2 T 0 15 0 2 7 San MuREEN 05 0 0 1 2 3 4 5 6 67 72 T7 82 Function of distribution i Function of distribution 0 8 1 5 0 6 0 4 1 4 0 2 0 5 0 0 ee 0 2 I 6 8 E EN NN NND ND ND ND ND HH 2 2 Choice and adjustment of probability laws A law of probability makes it possible to model a random variable To choose a law of probability as well as possible we proceed in the following way 1 Analyze the nature of the parameter discrete or continuous and its physical significance 2 Seek experimental data possibly censored sample operational data test results judgement of expert 3 Choose a law corresponding to the physical phenomenon if it exists or being able to represent the experimental data 4 Carry out an adjustment to find the parameters of the law corresponding as well as possible to the experimental data The maximum likelihood method is used by the tool for adjustment It consists in maximizing the product of the probability densities of the la
12. 1 Statistical Processing After selecting a simulation results sheet graph Command Statistics of menu Simulation enables to perform on results various statistical processing operations by ticking among various options proposed in a dialog box Example below shows results obtained for all such options El Graph Joj x Probability graph El Cost per unit Bl Launching cost O Number of sales D Price B Result 16000 32000 468000 64000 980000 STATISTICS E EY gt W Average 2 M standardDev Sample C Population B W Variance C Sample Population W Median En W Kurtosis Cost per Launching Humber of E v Asymmetry Coefficient unit cost sales 2 end RES o Average 24 9402655 3359 712412 216609505 36 2366598 24697 9743 rom um Iv Covariance matrix deviation 5 MS Median 24 35985536 3381 79924 2082 26494 37 5254656 23346835 2 Iv iagram of correlation between variables 7 ie fet Asymmetry 0 12483869 0 34137345 0 54261496 0 53613326 D 8535114 Number af sales Frice Launching cost Number of sats Confidence interval in 90 E Lamm ee OR Cancel 2451251 3273 58188 2013 58095 37 513056 22459 4619 252840211 3445 83226 2322 6007 36 9602636 27335 4867 Covariance Matrix BEN TTE E oe Diagram of Correlation Matrix of Linear Correlation Coefficients Cost per unit LU NR LE Price Result cost sales 1 O
13. Cab Innovation 3 rue de la Coquille 31500 Toulouse Tel 33 0 5 61 54 68 08 Fax 33 0 5 61 54 33 32 Mail Contact cabinnovation com Web www cabinnovation com SIMCAB Version 13 using Microsoft EXCEL ax Graph Jof x Distribution function Ey Sheet of computation Variable 1 08 Variable 1 Varlable z 05 Variable 3 04 Result 2 B e R sult2 E Graph Result 1 Probability graph Alilu 0 1 2 3 4 5 B 7 B 9 10 11 12 13 14 15 R sult 1 B R sult 2 Generic Monte Carlo Simulation Tool User s Manual FOREWORD The software SIMCAB BASIC version 6 includes some of the SIMCAB version 13 features It is not the subject of a specific user manual The copyright law and international conventions protect the SIMCAB software and its User s Manual Their reproduction or distribution either wholly or partly through any means whatsoever is strictly prohibited Any person who does not comply with such provisions is committing an offence of forgery and is liable to prosecution and can be sentenced under the provisions prescribed by the law The Programming Protection Agency A P P references SIMCAB at the I D D N Inter Deposit Digital Number index with the following reference IDDN FR 001 460001 00 R P 2000 000 20700 CONTENTS 1 SIMCAB Software 1 1 General Presentation 1 2 Installing SZMCAB on hard disk 1 3 Starting SIMCAB 2 Teachware 2 1 Re
14. Nm Input or result variables to be subject to a simulation are to be selected in left list including all preliminarily defined variable and result names A mouse click on one of names initiates such name in the right hand list of variables selected A mouse click on one of right list s names makes it disappear from the list hereof Clicking on the double arrow makes them all disappear The number of simulations required is limited to 16 000 The more such number is high the better the accuracy of results obtained but this is detrimental to the processing time Therefore it 1s recommended to start simulation with a low number 100 then carry on subsequently by increasing such number Results of simulation may be presented in frequency graph probability graph distribution function or distribution function Variables may be grouped up on a same graph or be subject to separated graphs 23 The probability to be in an interval can be estimated as that of obtaining a negative result Vmax 0 A confidence interval around the average value of each result can be evaluated according to a confidence level Two values of quantile upper Sup and lower Inf can be estimated either directly those of the simulated sample those of the population with a confidence level by applying the method of Wilks the lower bound for the lower quantile or upper bound for the upper quantile OK Initiating button ox runs therefore simul
15. SUPERCAB Software SUPERCAB is a dependability and safety tool Examples below illustrate the joint application possibilities offered with such software Ey Ex Sim_5 LL Of xj Reliability Block Diagram tCounbng wih Sunercab Taj UNITS MTTF Kinf of iab ud at Unit 1 Unit 2 hour redundancy 7 ears _ Assent Suececoee 0 51 016462 Mean value 0 589 passive 3 4 serie Standar deviation D 073 Scattering over the reliability of a system architecture Example hereof shows how this joint application helps initiating scattering on entries MTTF mean time to failure of a particularly complex processing reliability calculation of a system architecture assessed from automatically generated Markovian models S Exemple8 xls Availability of a mission with 2 satellites Lbd1 3 07153E 05 Lbd2 3 07153E 05 Sat 1 amp 2 ok Built duration 5360 547255 Sat1loss Launch failure Sat2loss Repearing duration 5360547255 Mission loss Mu 0000186548 INIT Availability 0 792282993 Mean value 0 744 Standard deviation Mission OK Markov matrix Scattering over a mission reliability Equally these last two examples illustrate this joint application possibility for a Markov matrix processing and an event probability assessment in a fault tree respectively E Ex_Sim_6 olx Fault tree ousting wih CABTAEE tof 4t ad BPA LF Mean value of event a probability 0 371 Standar d
16. al possibility to consider various probability laws of transition MAT INIT 0 8 0 2 0 0 ETATS 1 1 0 0 For this purpose the macro function MARK SIM are proposed by the tool to calculate the probability of being in the various states of the system or in a combination of states at the time T MARK SIM MAT INIT STATE T N The argument MAT corresponds to matrix of transition rates in hour 1 terms of main diagonal are automatically computed during the processing and empty cells are replaced by 0 Associated exponential laws the rates of transition can be replaced by other laws of probability as in the example above Nor 20 1 2 Normal Law of average 20 and standard deviation 1 while preserving at the system its Markovian character no memory after each transition Each of laws is defined by its first 3 letters followed by 5 arguments in brackets separated by a comma whose meaning is the same as those of random parametric functions to simulate various laws of probability on the spreadsheet Vector INIT corresponds to the probabilities of being in the various states at T 0 Vector STATE defines the combination of states to be evaluated state 1 or 2 in the example If this vector is not defined the tool calculates the probability of being in state 1 Argument N corresponds to the number of simulations to carry out before leading to the result MARK SIM function may be used in matrix form To do so select a range of
17. allows to estimate an upper bound or lower bound of a quantile with a confidence level B 90 This value Qag is equal to the data of rank r in size N sample defined by the Wilks formula N i i 1 C 0 a gt g For example the 95 95 quantile estimation of the temperature reached in a nuclear reactor in the absence of any cooling is used to size the ultimate barrier protection tubes of graphite surrounding the uranium 11 2 Methods of variance reduction The reduction of variance consists in privileging a field of interest during simulation then to balance the results obtained by application of the theorem of the total probabilities Y P Y P Y 1 P 1 P Y 2 P 2 Objective Increase the precision of the results confidence intervals Estimate the occurrence probabilities of rare events Decrease simulation duration The reduction of the variance can be implemented by various methods Variance reduction per stratified sampling Creation of layers squaring disjoined on the entries and random pullings in each one of these layers The estimate at exit is the sum of the estimates in each layer balanced by the probability that pulling of it results E Pulling are carried out even in the least probable zones The layers can be equiprobable even probability equidistant even size or personalized when we know the zone of interest to privilege 12 Variance reduction per sampling o
18. ation and controls the requested results display as shown in examples below Ej Graph 1 il x Probability graph Average 2 65E 04 Standard deviation 1 93E 04 Confidence interval in 60 2 60E 04 2 70E 04 E Graph O x Probability graph E Price Bl Cost per unit 24 E Graph BI Distribution function Average 2 62E 04 Standard deviation 1 80E 04 1 2 1 0 6 0 4 0 2 S 1000 15000 31000 47000 63000 79000 95000 111000 These different charts are accompanied by following dialog box which allows to carry on simulation doubling of number of achieved simulations is proposed by default to modify results overview or to perform on results various statistical processing shown in chapter 3 5 SIMCAB Fx Are you willing Continue simulation 2000 Cancel Modify results display Statistics Pressing button Mody results display initiates the display of following dialog box allowing to modify the type of graph selected modify minimum and maximum limiters as well as the viewing step and possibly request the confidence interval display SIMCAB ea C Frequency graph Scale Probability graph step 4000 Distribution Function Y min lo LU 100000 C Distribution Function 1 umm iis Confidence interval in os OK Delete Modifying one of limiters initiates the display on graph of probability that variable be beyond that limiter as shown in such example where pro
19. bability that result be a loss is thereby immediately provided 25 E Graph 1 Iof x Probability graph Average 2 67E 04 Standard deviation 1 78E 04 lt 0 0 00475 100000 0 00175 16000 S4000 40000 64000 S d SOO Remarks All graphs obtained are in specific calculation sheets which include all results of relevant simulation Performing the simulation initiates the creation of two additional names for each variable defined as result Average_Result and Standard_Deviation_Result which correspond to the average value and standard deviation of variable with name Result respectively Such names are specially used for optimization purposes See chapter 3 4 In the same way the names CMax Result CMin Result Confidence rate and Nb simu are also created if the calculation of the confidence interval is required These names correspond respectively at the lower and higher boundaries of the confidence interval the corresponding rate and the number of simulations carried out Finally the names quantile inf R sultat quantile sup R sultat Quantile inf and Quantile sup and Confiance quantile are also created if the calculation of quantiles is requested These names correspond to the values of the quantiles of the distribution of results for the corresponding lower and upper quantiles possibly considering a confidence level by applying the method of Wilks 26 3 5 Statistics 3 5
20. call on the statistics 2 2 Choice and adjustment of probability laws 2 3 Principle of the Monte Carlo simulation 2 4 Control uncertainties by Monte Carlo simulation 2 5 Concept of confidence interval 2 6 Quantile 2 7 Methods of variance reduction 2 8 Simulation of random variable 2 9 Recursive Modeling 2 10Simulator of system architecture 3 Application 3 1 Defining a variable 3 1 1 Adding Deleting Displaying 3 1 2 Setting 3 1 3 Personalized Function 3 2 Defining a Result 3 3 Using Names 3 4 Executing Simulation 3 5 Statistics 3 5 Statistical Processing 3 5 2 Meaning of Processing Operations 3 6 Treatment of the dynamic systems 3 6 1 Recursive Modeling 3 6 2 Simulator of system architecture 3 6 3 Simulation of Markovian systems 4 Applications and Joint Application Possibilities 4 1 Controlling uncertainties 4 2 Simulation 4 3 Joint Application With SUPERCAB Software 4 4 Joint Application With GENCAB Software 5 Features of Probability Law OPERATING LICENCE AGREEMENT 1 SIMCAB Software 1 1 General Presentation SIMCAB is a generic Monte Carlo simulation program which helps supplementing spreadsheet with random variables so as to enable any user to control dispersions in computations or efficiently simulate varied problems Using a menu offered by program the user defines the names and features of random variables used in his computation and designates sheet cells containing results So he may initiate s
21. cted to wear according to a Weibul law D 5 Y 0 o 4000 and replaced periodically 3000 hours after TO and preventive or corrective maintenance actions Possibility of choosing the number of repairers per subsystem of 1 to N with evaluation of the particular case 1 repairer for subsystem 2 and 3 repairers for the subsystem 3 Taken into account of a production request modified every 2000 hours on average and distributed uniformly between 60 and 130 evaluation of the proportion of the really satisfied request Compared to MINIPLANT MINIPLANT Pro considers cost data in order to optimize the means of production e The maintenance cost of the A element is one cost unit annual Cost 760 Period of maintenance e The annual depreciation of each set A C1 C2 B1 B2 E1 E8 is 10 cost units for their initial capacity that is to say respectively 100 40 30 and 15 and 1s proportional to this capacity which can be modified in a ratio from 0 5 to 2 e The annual cost of each repairer of the sets C1 C2 BI B2 and E1 E8 is 1 cost unit c Model of satellites constellation deployment and maintenance The constellation consists of N operational satellites plus spares 15 to the maximum simultaneously in orbit Those can break down and have each one a limited lifespan due to their propellant capacity Ej CONSTELLATION xis E 2 lal x Sat OK LO OP Constellation of satellites T i deltaT i Tmission Lo
22. duction whose capacity is equal to lowest capacities of three subsystems in series e Each block contributes to the output of the unit of which it forms part The blocks Cl and C2 are in cold passive redundancy C2 functions only in the event of C1 failure with a null failure rate to the state OFF and the E1 E8 blocks function only so at least 6 of them are operational in order to exceed a minimal threshold of 90 of capacity for this last subsystem e Two policies of maintenance are considered a repairer per block or only one repairing per subsystem with repair of the blocks in the order of appearance of the failures a Tmission orgi A m Capacity DeltaT 2E 05 0 005 100 AO 22 C1 10 0001 0002 40 3028 Single repairer Production 100 Average production mission Probability graph Trepairer Probability graph N repairers Average 9 34E 01 Standard deviation 5846 0 Average 94 E 01 Standard deviation 5 36E 02 Confidence interval in 90 9 33E 01 9 35E 201 Confklence interval in 907 46E 01 9 48E 01 0 6 0 05 o HH EEU i 33 MINIPLANT differs from the MINIPLANT test case by the following elements Introduction of a stochastic dependence The C2 element of the cold redundancy is affected of a failure rate AOFF AON 10 and of a failure rate to the request y 1 Introduction of a phenomenon of wear and a periodic maintenance it is added to element A an element A in series subje
23. erval The confidence interval makes it possible to evaluate the true value of a parameter on the basis of result of simulation or observations carried out on a sample The confidence interval at the a risk contains the value of the parameter with probability 1 ot True value l Proba 0 2 B Min Average 1 Bmax 0 2 Defined by the central limit theorem it is all the more narrow as the variance standard deviation 1s weak and that the size NR of the sample a number of simulations is large Or in the case of a proportion with Uon u 1 0 2 the reverse of the function of distribution of the reduced centered normal law Demonstration Evaluation of the average of a Lognormale law 0 14 0 12 0 1 0 08 0 06 0 04 0 02 0 Lognormale a 4 b 0 5 Moyenne 61 8 Ecart Type 32 6 av O O A amp X q d d oo L Q 61 8678093 E a 4096 a 1096 a i 2 b N 1000 m 61 77 sigma Confidence intervals at 60 and 90 10 2 6 Quantile A quantile is the value that separates the data distribution in a certain proportion Quantile function is the inverse of the distribution function Quantiles from 1 to 99 are called percentiles Quantiles 10 to 90 are called deciles Quantiles 25 50 and 75 are called quartiles The 50 percentile is the median The quantile X is a variable value that the probability of passing through is X Wilks method
24. eviation 0 012 Scattering on probability of an event 43 4 4 Joint Application with GENCAB software Such a coupling enables to achieve optimizations from simulation results Sri Parking strategy Nth free space or first free space after row P T 10 spaces per minute rip 3 ER Free space 1 19 Free space 2 496 P NN f BUE x Free spaces s N A Free spaced zM A M 5 15 minutes Free space 5 gM A Free space b zM A P hb Free space f M A Free space B M A Space number gh Free space 8 M A Free space lll M amp Time taken to reach the objective 1 36 minutes Mean value 47259 Standard deviation 3 09317466 In this example the two optimal parameters of parking strategy Nth free parking lot and row P from which the first free parking lot will be systematically taken are being searched by GENCAB by minimizing the average of times taken to reach the objective assessed by SIMCAB This joint application possibility may help dealing with different types of problems So it becomes possible optimizing parameters of an intervention strategy on a system subject to simulation command control traffic management maintenance 44 5 Features of Probability Laws The different software proposed probability laws are briefly described in this chapter Binomial Law Binomial law represents the number of successes obtained after n independent tests each one with a probability p
25. f tmportance Use of a function of importance to encourage pullings in the interesting zones to reach CCS 2 28000 eee aaa o amp The weight which is given to each simulation is the ratio between the density of probability of the random function and that of the function of importance 2 8 Simulation of random variable Performed by the tool the simulation of a random variable can be carried out in the following way Function of distribution X X 1 Draw a random values u between 0 and 1 2 Apply from this value the opposite function of the function of distribution if it exists 3 In other cases specific algorithms can be use A random generator is an algorithm which allows creating lists of numbers uniformly distributed between O0 and 1 The numbers should not be correlated and the period of the list must be largest possible T Simcab gt 1 000 000 The tool proposes parametric random functions allowing simulating the following laws BETA BINOMIAL ERLANG EXPONENTIAL GAMMA GEOMETRICAL GUMBEL HYPERGEOMETRIC LOGNORMAL NORMAL PARETO PEARSON PERSONNALIZED POISSON TRIANGULAR UNIFORM WEIBULL with 2 or 3 parameters The format of these functions is L_EXP with EXP the first 3 letters of the considered law 13 Demonstration Simulation of an exponential law Ey DIDAC_6B Example Exponential law F x 1 exp lambda x 1344 14 161 42 Lambda 0 003 Exponential law Func
26. greement is entered into for an undetermined period of time as of the date set forth in Article 3 ARTICLE 9 TERMINATION Each party may terminate this Agreement by registered mail with acknowledgement of receipt forwarded to the other party for any breach by such party of its obligations despite a notice remaining unresponsive for 15 days and this occurring with no prejudice to damages it could claim and provided that the last paragraph of Article 7 above be enforced At end of this Agreement or in case of termination for whatsoever reason the customer will have to stop using SIMCAB software package pay all sums remaining due on date of termination and return all elements composing the software package computer programs documentation etc without maintaining any copy of it ARTICLE 10 ROYALTY As a payment for the operating right concession the customer pays CAB INNOVATION an initial royalty the amount of which is determined in specific conditions ARTICLE 11 PROHIBITED TRANFER The customer refrains from transferring the software package operating right granted personally to him by these provisions The customer also abstains from making documentation and supporting material CD ROM even free of charge available to a person not expressly set forth in second paragraph of Article 2 ARTICLE 12 ADDITIONAL SERVICES Any additional services will be subject to an amendment of these provisions possibly through an exchange of le
27. icient of flattening of simulation results A positive Kurtosis corresponds to a relatively thorough distribution compared to a normal distribution A negative Kurtosis corresponds to a relatively flattened distribution compared to a normal distribution Asymmetry Coefficient Enters the asymmetry coefficient of simulation results which features the non symmetry of distribution with respect to median A positive coefficient corresponds to a distribution shifted towards positive value section A negative coefficient corresponds to a distribution shifted towards negative value section Confidence Interval Interval which includes the considered parameter with a probability equal to confidence level Confidence interval depends on sample size number of simulations and on standard deviation of this sample 28 Covariance Matrix Covariance features the linking intensity between two parameters arithmetic average of products of deviations for each of them Enters the covariance matrix between the various simulated parameters Matrix of Linear Correlation Coefficients This coefficient features the linking linearity between two parameters Enters matrix of linear correlation coefficients between the various simulated parameters This coefficient may vary between and 1 Diagram of Correlation Between Variables Enters diagram of correlation between two selected parameters cluster of points typical of couples xi and yi being
28. imulation then display the graph results frequency graph probability graph distribution function and using them perform various statistic processings average median typical deviation kurtosis asymmetry confidence interval correlation Many probability laws are offered by the program Beta Binomial Erlang Exponential Gamma Geometric Gumbel Hypergeometric Lognormal Normal Pareto Pearson Personalized Poisson Triangular Uniform Weibull which can be adjusted by the program from experimental data using maximum likelihood method SIMCAB allows processing recursive simulation models in order to assess dynamic and hybrid systems with continuous and discrete variables A function of simulation of Markovian systems is also proposed by the tool In addition SIMCAB can be jointly used with the other tools of CAB INNOVATION either to control scattering in assessments performed by the software of Reliability SUPERCAB and CABTREE or to achieve optimizations by means of tool GENCAB starting from the simulation results 1 2 Installing S MCAB on Hard Disk Please follow instructions shown in manual 1 3 Starting S MCAB In EXCEL open SIMCAB XLA file Software s functionalities are then accessible using menu Simulation spreadsheet functionalities remaining always available SIMCAB V 10 Cy jid C Classeur2 Accueil Insertion Mise en page Formules Donn es Revision Affichage Simula
29. l 12 14 1 Avail 13 16 1 Avail 14 16 1 Success f 1 Success 2 1 Success 3 1 Success 4 1 Success hb 1 Success b 1 Success T 1 Success amp 1 Success 9 1 Success 10 1 Success 1 1 Success 12 1 Success TX 1 1 Success 14 Loss 14 Performance T a a Time Tears Launchers Lambda 2 092E 05 Launchin Launch a 35 Launch b 4 5 Launch c 7 09 Launch d 3 5 Launch e 115 Launch F 14 1 Launch g 16 1 Reliability 0 37 Mission Success of Launching Perak 025 033 037 0 39 Pertoz 43 92 we 128 Perfos 54 33 4d gd Success a Success b Success 0 Success d Success e Success F Success g Perfo 0 361 Cost 197 31 Average Perfo 0 353 Average Cost 137 33 Average Cost per gear 13 65 Sigma sigma sigma Cost by 6 month old section MEuros with TO Time pears Scenario 22 40 2 no spare with anticipation Ground action After 1 failurefneed or at the end of lifetime Performance Rate of realization From 4 5 to 14 5 years From D bo 14 5 years 0 018 10 15 r This more complex example shows how the performances and the costs of a constellation of satellites can be simulated by considering various strategies of deployment and renewal Also proposed in demonstration by the tool this example required the development of a specific macro function which makes it possible to identify the nth value in a list Order list N 4 3 Joint Application with
30. logical description of nominal or degraded mode of operation The operating conditions and the conditions maintained in the passive state are defined using the operators AND OR NOT and combination m among n m n i k Given by default the exponential can be replaced by other laws of probability considering or not the Markov assumption The tool can also draw the Reliability Block Diagram RBD animated by the simulation step by step or as a picture 15 3 Application The user defines its processing on a calculation sheet using parameter names corresponding to random variables of which he specifies the features using menu Define a variable Then he designates sheet cells containing results using menu Define a result Afterwards he runs the simulation using menu Execute then he displays the graph shaped results He may achieve various statistical processing on results using menu Statistics Menu Use names helps entering formulas in sheet s cells by using preliminarily defined result or variable names without having to enter them again Menu Define a variable helps also display different software proposed probability laws know their operating conditions using an online hotline and perform settings on them from experimental data 3 1 Defining a variable Command Define a variable of menu Simulation allows to display dialog box below DEFINE A VARIABLE Used variables Launchi
31. m Surface of the circle II 0 5 0 785 m i t e ai 127 impacts in the target on 1000 The surface of the figure 1s 6 127 1000 0 762 m The value of II is approximately 3 048 2 4 Control uncertainties by Monte Carlo simulation Monte Carlo simulation allows evaluating uncertainties in a calculation while proceeding in the following way Random variables 4 Lx KLI LAX J X X 1 2 Y n 1 Make a random drawing of the entries in accordance with their statistical distribution 2 Inject the values of these entries in calculation in order to obtain a result 3 Reiterate the operation a great number of times in order to obtain a distribution of result Easy to implement the simulation of Monte Carlo allows carrying out analyses of uncertainty or sensitivity It guarantees the covering of the worst cases which are not always easy to identify Statistical distribution is much richer than a simple average value because it makes it possible to calculate the probability that the result 1s included in an interval Demonstration Uncertainty over the duration of a way V 2525 Em hr Le 100 Km o 1 Lenath L Time T The probability that the journey time is lower than 4 hours 30 is 0 78 The function of distribution obtained by simulation makes it possible to evaluate the probability that the result is lower than a certain value or included in an interval 2 5 Concept of confidence int
32. n may be entered by yourself or generated directly by software From a chronological series State address of matrix s upper left cell in box below 0 07692308 E 60 E 15384515 Specify if applicable address of chronological series in box below F 44 F 56 s select to do so relevant cells OK Cancel D 538461 54 0 61538462 0 92307692 vr M4 bi Feuilt Feuil2 Feuils f 20 3 2 Define a result This operation consists in allotting names to calculation sheet cells and consider them as processing results Command Define a result of menu Simulation allows to define a result using a dialog box identical to that used to define input variables Its application is illustrated in example below E EX SIM 1 XL5S Launching of a new product Launching cost 3858 85 Price 31 83 Number of sales elie Cost per unit 3 60 Result 57592 3691 DEFINE A RESULT Defined results Mame Refers En scga s iE 5 De Active cell address is proposed by default in dialog box as well as any possible name written out on sheet close to the latter Ok Buttons Ret Add and Pete are used just the same way as those of dialog box Define a variable 2 3 3 Using Names Command Use names of menu Simulation enables to enter formulas in sheet cells by using preliminarily defined variable or result names with no need to re enter them
33. ng cast Report Number of sales Price Mame Cost per unit Type of law NORMAL BETA BINOMIAL 5 deviation Umit Maximum 16 3 1 1 Adding Deleting Displaying Defining a variable consists in giving a name to it in box Name Cost per unit in the example choosing the relevant statistic law in a scrolling list Normal informing the value of law s parameters Average 25 Standard Deviation 3 in relevant boxes which are OK displayed depending on law selected then pressing button or button ut if a list of numerous variables 1s to be successively defined In order to simplify the entering the parameters of the laws can be them even defined by parameters of the spreadsheet Value 25 for example will be replaced by the name Average which itself will be given to a cell of the spreadsheet Minimum 0 and maximum 100 limiters for values likely to be assumed by variable as well as its unit may be also defined in relevant boxes A name mentioned on sheet close to active cell is proposed by default as a variable name in dialog box In one compound name linking symbol is automatically added up by software when validated Cost per unit Cost per unit A value is allotted to the variable name as soon as the latter is defined and its name is added up to the scrolling list of variables being used Activating the latter helps display the features of preliminarily defined variables But
34. numbers preceded by the letter E or other operating conditions preceded by the letter F 36 DeltaT Ti Equipments TTF TTR TTS E1 12178 69 E2 E3 E4 E5 E6 E7 0 00 E8 000 E9 ooo Stocks TAT S NN E S4 Operations F1 F2 F3 F4 Average mission F1 Markovian is Simulator F4 The state of equipments stocks of spare and functions appear in 3 columns corresponding to time TO Ti and Tj The active state is characterized by the value 1 green the state of failure by the value 0 red and the passive state by the lack of character grey The central cells blue correspond to the time before failure TTF before repair TTR before transition to active or passive state TTS or before restocking the spare TAT Additional cells are also used to calculate the average availability of different functions during the mission For non Markovian additional lines are added to each equipment as either repairable or passive with reconfiguration duration and to each item of spare stocks that supply is independent TO Ti Equipments TTF TTR TTS E1 ERI 747 58 5 E3 87 44 0 00 E4 E5 E6 E 000 E8 O00 E9 61981 72 0 00 Stocks TAT S1 NN ipm S NN pem Non Markovian 37 3 6 3 Simulation of Markovian systems Same manner that tool SUPERCAB SIMCAB makes it possible to simulate the matrices of Markov while offering the addition
35. on a line Triangular Law The Triangular law is featured by values taken between two limiters minimum and maximum the probability of which decreases linearly depending on distance at a probable value Example Prediction of a product s sale Uniform Law The Uniform law is featured by equiprobable values taken between two limiters minimum and maximum Example Frequencies of a random noise Weibull Law The Weibull law with 2 or 3 parameters may describe many distributions depending on values of its parameters Example Time of proper operation of an equipment with a variable failure rate mechanical equipment undergoing a wear 46 OPERATING LICENCE AGREEMENT OF SIMCAB SOFTWARE PACKAGE ARTICLE 1 SUBJECT The purpose of this Agreement is to define the conditions in which the CAB INNOVATION Company grants the customer with a non transferable non exclusive and personal right to use the software package referred to as SIMCAB and whose features are specified in user s manual ARTICLE 2 SCOPE OF THE OPERATING RIGHT The customer may use the software package on one single computer and on a second one provided that the second computer does not operate at the same time as the first one The customer can only have one software package copy maintained in a safe place as a backup copy If this license is regarding a performance on site the customer may install the package software on a server while scrupulously com
36. onth validity During the guarantee validity if the customer experiences a software package operation trouble he should inform CAB INNOVATION about it so as to receive any helpful explanations with the purpose of remedying such trouble If the trouble is continuing the customer will return the C D ROM to CAB INNOVATION at CAB INNOVATION s Head Office at his own expense and with registered mail with acknowledgement of receipt by specifying exactly the troubles encountered Within the three months of reception of consignment set forth in preceding paragraph CAB INNOVATION will deliver at its own expense a new product version to the customer This new version will be benefiting of the same guarantee as benefited the first version The customer looses the benefit of the guarantee if he does not comply with the instructions manual recommendations if he performs modifications of configuration set forth in Article 2 above without obtaining a prior written consent from CAB INNOVATION or if he performs modifications additions corrections etc on software package even with the support from a specialized service company without obtaining a prior written consent from CAB INNOVATION ARTICLE 5 PROPERTY RIGHT CAB INNOVATION declares to be holding all the rights provided for by the intellectual property code for SIMCAB package software and its documentation As this operating right granting generates no property right transfer the customer ab
37. or during a complete mission which is simulated a great number of times in order to reach the required precision 30 b Implementation Command Recursif Model of Simulation menu allows getting the following dialog box used to define the addresses of the various cells defining the states Eo E and E and the increments of time as well as the duration of the mission RECLIRSIF MODEL Construction af a recursive model of Monte Carlo simulation Addresses of the cells defining states ED Ei Ej with TO B 6 B415 Ti C 6 5C415 Ti 0 6 D 15 Addresses of the cells defining the increments of time dT 8 17 B8 22 E 27 g You can select the cells with the mouse and the key Ctrl iF several beaches of cells are concerned Duration af Ehe mission 500000 Temporization after each event second D al il v Addition of buttons of activation and test 2 j OK Cancel Each address of cells can be broken up into multiple secondary addresses by the use of the mouse and the key Ctrl Button of activation and test initialization step by step simulation can be copied on the sheet in order to facilitate the validation of the model and a temporization after each event can be required in second INIT parameter is also created in the worksheet to facilitate the development of the model of simulation This one is with the True state with initialization then with the False state during simulation To allo
38. ows the regulation of liquid level in a tank at a minimum or maximum threshold according to relative flows between the filling pumps and the emptying valve These components are reparable and have each one 2 possible modes of failure blocked ON or OFF for the pumps and blocked in the current state Open or closed for the valve 2x RESERVOIR XLS To Ti Tj Pump 1 j 0 35721886 38528 507 T temps courant hi n h height of water m 1 Ok 2 bloqued ON 3 bloqued OFF Max threshold 1 Ok 2 bloqued ON 3 bloqued OFF 1 Ok 2 bloqued Open 3 bloqued Closed Nbovfiw 0 0 0O Curmulated number of overfiows SSH Cumulated duration of overflows hr Initialisstion Lost cumulated volume m3 Valve Cumulated numbers of emptyings Step Cumulated duration in emptying hr Cumulated volume not provided Simulation PumoiNOK MURPI SEU ePi T 0000 Pumpi Pump2 WValve Pump 2 OK h gt Maxthreshold stopped stopped Open Pump2 NOK MIRP2 500 pP2 00002 Max threshold 2h 2M nthreshold active stopped Open h Min threshold Vae Nok mmv 10000 aV 0 01 Tank surface m2 50 Sr A flow 0 lh Tank height m 6 Hr dh dt 0 m h Min threshold m 2 Smin hehreshoid 2 00 Max treshold m 4 Smax Tinreshoid SoHE Pump flow 1 l h Pump flow 2 l h Valve flow l h 22 b Capacity of production Miniplant test case MINIPLANT relates to a factory of pro
39. per left cell provide information about input formats 35 As an illustration the example of a cement plant below is presented in the online help Ne Name 1 Bi Law Conditiona Law hore Law Tucu y M 1 Excavator EXP o001 EXP 002 fee EeP 2 EXP 1000 E ME Exe ooo Exe Loos XE ee 3 Escavator3 EXP 0 0001 EXP 0 02 t 2 EXP 1E 06 EXP 1 oo 1 EXP 5 6 Crsher2 EXP 7E 05 EXP 0 002 EXP JEXP EXP 3 1 2 3 4 5 EXP _ 1E 06 EXP 24 1 EXP 8 Crusher3 EXP 7E 05 EXP 0 002 3 1 2 3 4 5 EXP 7E 07 EXP 24 4 EXP 9 Kin2 EXP 5E 05 EXP 0 0033 3 1 2 3 4 5 EXP _ 5E 07 EXP 24 J EXP Operation N Name y OCondtion S O 2 3 E1 E2 E3 E4 E5 E6 1 3 E1 E2 E3 E4 E5 E6 E7 E8 E9 The conditions maintained in the passive state are defined from the operative state no failure of equipments identified by their number Thus the excavator 3 is not used when the first 2 work It is operational after an hour with a solicitation failure probability of 1 It uses the same stock of spare equipments that 1 which consists of 2 units with a restock time of 1000 hours The equipment order in the table defines the allocation order of spares in case of a stock split and it is decremented at the end of each repair The operating conditions are defined from the activation state ON state of equipment identified by
40. plying with purchase conditions stated on specific conditions especially defining the maximum number of users authorized to use the software package from their terminal and the maximum number of users authorized to use it simultaneously The customer is therefore authorized to perform a number of software package documentation copies equal to the maximum number of users allowed to use it CAB INNOVATION will be in a position to perform inspections either itself or through a specialized entity purposefully authorized by CAB INNOVATION at customer premises to verify if customer has met its requirements number of software package copies used location of such copies etc Parties will agree as regards the practical modalities of performance of such inspections so as to disturb minimally customer s activity ARTICLE 3 DELIVERY INSTALLATION AND RECEPTION The software package and attached supplies will be delivered to the customer on mail reception date The customer installs at its own costs the software package using relevant manual delivered by CAB INNOVATION The customer performs the inventory and shall inform CAB INNOVATION within three working days of the delivery of any apparent nonconformity with respect to the order The customer is liable for any loss or any damage caused to supplies as from the delivery ARTICLE 4 TESTING AND GUARANTEE Guarantee is effective as from the mail delivery date set forth in Article 3 and has a three m
41. robustness of one design in the worst cases of operation 40 This second example illustrates a highly classical range of problems regarding design that is how to make sure that design will be robust in the worst cases of nominal operations assuming components going downhill power supply variations ageing radiation doses received etc E PME Dispersions of resistance and stress Probability of breaking S gt R 0 3 E Stress B Resistance How to dimension properly a safety margin This third example finally shows how in mechanics a dimensioning assuming dispersions of materials resistance and stress undergone provides a much better guarantee than if it is only based on using a simple safety coefficient ratio between average resistance and average stress 4 2 Simulation In addition to the assessment of scattering in calculations whose purpose is controlling uncertainties simulation may also enable to face difficult results even impossible to get through analytical computations So examples below show simulations achieved in the Operation Safety field E EX SIM 3 XLS Reliability assessment MTBF E1 E2 E3Y Ours MTBF off 10 MTBF on Lambda on 0 00005 Operating duration of redundancies Lambda off 5E 06 Serie 1669 Operating duration 39326 Parallel 39326 Reliability 1669 3484 74333 Parallel Vote 2 3 39326 Passive Sere Vote Passive 40995
42. rov Smirnov 0 62 D5 1 35 Experimental dat WEIBULL C Quantile quantile diagram Adequacy graph Preserve the graph The diagram quantile quantile and other graphics Weibull paper to visually judge the adequacy of the model are proposed for the user 19 Feuil3 Quantile quantile diagram Weibull paper In In 1 1 F t 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 l Experimental data In t qgamma Feuill KI Feuil1 E If setting is accepted by user dialog box Define a variable is newly displayed with optimal parameters of the informed law 3 1 3 Personalized Function Main features of software proposed probability laws are set forth in Section 4 of manual hereof However a specific law called Personalized helps user define any law by entering directly its distribution function on processing sheet or by having the latter generated by software from experimental data After pressing button 2 it specifies to do so the address of sheet where the distribution function of such law can be found as in example hereunder cost variable and possibly the address of chronological series if function shall be initiated E Classeur OS E HELP PERSONALIZED LAW x Such Functionality allows you to define any type of statistical law From its distribution Function defined an processing sheet Defined by a z column matrix values and growing probabilities From O En 13 such Functio
43. stains from any SIMCAB software package reproduction whether it is wholly or partly carried out whatever the form assumed excepting the number of copies authorized in Article 2 any SIMCAB software package transcription in any other language than that provided for in this Agreement see Appendix any adaptation to use it in other equipment or with other basic software packages de base than those provided for in this Agreement To ensure this property protection the customer undertakes especially to 47 maintain clearly visible any property and copyright specifications that CAB INNOVATION would have affixed on programs supporting material and documentation assume with respect to his staff and any external person any helpful information and prevention step ARTICLE 6 USING SOURCES Any SIMCAB software package modification transcription and as a general rule any operation requiring the use of sources and their documentation are exclusively reserved for CAB INNOVATION The customer holds the right to get the information required for the software package interoperability with other softwares he is using under the conditions provided for in the intellectual property code In each case an amendment of these provisions will set out the price time limits and general terms of performance thereof ARTICLE 7 LIABILITY The customer is liable for choosing SIMCAB software package its adequacy with his requirements precau
44. t where it is translated into one or more foreign languages only the French text will be deemed authentic in case of any dispute between the parties ARTICLE 18 APPLICABLE LAW DISPUTES The French Law governs this Agreement In the event of any disagreement over the interpretation and performance of any whatsoever provision of this Agreement and if parties fail to reach an agreement under an arbitration procedure only Toulouse s Courts will be competent to settle the dispute despite the plurality of defendants or the appeal for guarantee 49
45. tion a3 Help Teachware E Define a variable c1 Execute a Recursif model i Other menus E Define a result dl Statistics gg Use names General Modeling Al a f kn P e 210 c 10 D d a d aa d a E a Simulation States system modeling Banner on Excel versions after 2007 EJ SIMCAB V 10 Classeur sH Fichier Edition Affichage Insertion Format Outils Donn es Fen tre Simulation Help Teachware Other menus Define a variable Define a result Use names Recursif model Execute Statistics Menu on Excel versions prior to 2007 Teachware and help are proposed in menu with many examples of application 2 Teachware The teachware presents the bases of the simulation of Monte Carlo by means of various figures and demonstrations 2 1 Recall on the statistics A random variable X is a variable resulting from a random phenomenon which admits a measurement of probability It can be discrete value obtained during a pulling of dice or continues size of a population Probability Disert Density of Continuous probability P X xi f x X x x dx xi Each possible value of a discrete variable can be characterized by a probability value p 1 6 for the 6 faces of the dice Each possible value of a continuous variable can be characterized by a density value of probability f x such as the probability that the random variable X ranging between x and x dx is equal to f x dx when dx
46. tion of distribution of i 3194 Function of distribution the simulated law i pies 5 8b u 0 7670497 1000 1500 1000 1500 X 485 64341 In 1 u lambda 2 9 Model of recursive simulation This is an original modeling technique of the discrete states systems A min Ty h oon f x The model of recursive simulation describes a generic transition from the states Ei at t1 to Ej at tj Its treatment consists in reinjecting in entry the state at exit starting from an initial state as many time as it is necessary to cover the mission The increment deltaT from ti to tj 1s the smallest computed value among various increments of time Tk These durations can correspond to deterministic or random changes of the system state failure repair or the crossing of thresholds by continuous variables in the case of the hybrid systems 14 2 10 Simulator of system architecture This tool can automatically generate a model of recursive simulation from a table filled in by the user Architecture Passive Simulator Spare RED Equipment Failure Repair Passive Stock of spare WT Ree Raw Tae e edis Law ar Caw aly PREYS e YA ae EPI EXP Operation W Name Condition y y O FE T eee pj EMEN A ee es c MMMMc2552WwWauac x EN The table includes the characteristics of failure repair reconfiguration and logistic of the system components and a
47. tions to be assumed and back up files to be made for his operation his staff qualification as he received from CAB INNOVATION recommendations and information required upon its operating conditions and limits of its performances set forth in user s manual the use made for results he obtains CAB INNOVATION is liable for the software package conformity with his documentation The customer shall prove any possible non conformity CAB INNOVATION does not assume any whatsoever guarantee whether explicit or implicit relating to the software package manuals attached documentation or any supporting item or material provided and especially any guarantee for marketing of any products relating to software package or for using software package for a determined use any guarantee for absence of forgery etc Under no circumstances CAB INNOVATION could be held responsible for any whatsoever damage especially loss in performance data loss or any other financial loss resulting from the use or impossibility to use the SIMCAB software package even if CAB INNOVATION was told about the possibility of such damage In the event where CAB INNOVATION liability is retained it is expressly agreed upon that the total amount of compensation to be paid by CAB INNOVATION all cases taken together could not in any way exceed the initial royalty price reduced by 25 per period of twelve months elapsed as from the mailing delivery date ARTICLE 8 DURATION This A
48. tomatically generate a model of recursive simulation from a table filled in by the user Architecture Passive Simulator Spare RED Equipment Failure Repair Passive Stock of spare n Ni Name Em baw Conditionarr aw ee Cow fd r T e jer Tee fer w Name Condition O Ee a NEEEEMEMEMEMEMEMEMEMEMEMESS ZzZ IE ZZI S bEL INSBMISMWAEBBNBNBNAESNAENSSAAAMALAL7AL7ZALAZAMZAMZAMN ee Bk E o o ol E a ns The table includes the characteristics of failure repair reconfiguration and logistic of the system components and a logical description of nominal or degraded mode of operation The operating conditions and the conditions maintained in the passive state are defined using the operators AND OR NOT and combination m among n m n i k Architecture __ Passive Simulator spare Equipment Failure Repair Markov wo omm USS ew e Given by default the exponential probability law can be replaced by another law Then additional columns allow to enter the law parameters and to indicate if the Markov assumption must be maintained for the equipment The buttons Passive and Spare can hide or show the relevant columns in the table The button Simulator allows to generate the simulation model and the button RBD draws the Reliability Block Diagram as a fixed picture or animated by the step by step simulation Many messages accessible by the mouse red dots in the up
49. ton Delete allows to delete a preliminarily defined variable selected in scrolling list Report _ l Button allows to generate a document containing all characteristics of the variables and results previously entered E Feuil2 VARIABLES NAME LAW PARAMETER 1 PARAMETER PARAMETER 3 MIN MAX UNIT NORMAL 25 2 oo Launching cost TRIANGULAR 3s 20004500 GF Number of sales TRIANGULAR 1500 o0 1 200 5000 TRIANGULAR 3 PY RESULTS NAME ADDRESS UNIT RIUC3 o 0 17 Button ove allows to perform a simulation of selected law then to display the results thereof as in example below Fy Feuil4 Probability graph Average 25E 00 Standard deviation 3E 00 006 UO Ob 104 O02 Cost per unit Button 2 allows to initiate an online hotline specifying the operating conditions of selected law as shown in example thereafter HELP Normal law represents many natural phenomena Featured by a variable likely to deviate symmetrically with respect bo an average value with a decreasing probability So the standard deviation corresponds to the average of deviations Example deviation between size of parts achieved and predicted size 3 1 2 Setting Button ass allows to set the law selected from experimental data When activated it initiates the display of the following dialog box which helps user inform the chronological series address through a selection
50. tters so as to specify the contents modalities of achievement and the price ARTICLE 13 CORRECTIVE AND PREVENTIVE MAINTENANCE 48 The corrective and preventive maintenance may be subject upon customer s request to a separate Agreement attached to these provisions ARTICLE 14 ENTIRETY OF THE AGREEMENT The user s manual defining the SIMCAB software package features 1s appended to these provisions The provisions of this Agreement and his Appendix express the entirety of the Agreement entered into between the parties They are prevailing among any proposition exchange of letters preceding its signing up together with any other provision stated in documents exchanged between the parties and relating to the Agreement s subject matter If any whatsoever clause of this Agreement is null and void with respect to a rule of Law or a Law in force it will considered as not being written though not involving the Agreement s nullity ARTICLE 15 ADVERTISING CAB INNOVATION could mention the customer in its business references as a SIMCAB software package user ARTICLE 16 CONFIDENTIALITY Each party undertakes not to disclose any kind of documents or information about the other party that it would have been informed of on the Agreement s performance and undertakes to have such obligation fulfilled by the persons it 1s liable for ARTICLE 17 AGREEMENT S LANGUAGE This Agreement is entered into and drawn up in the French language In the even
51. w considered for the values of the experimental data This product is multiplied by the probability of non occurrence for the censored data The quality of the adjustment carried out can be evaluated by various statistical tests Khi 2 Kolmogorov Smirnov Those give a measurement of the difference between the function of distribution of the law considered and that of the experimental data Demonstration Adjustment of various laws of probability starting from randomly values SET Khi 2 0 313 Kolmogorov Smirnov 0 077 2 0 8 0 6 0 4 Experimental data BETA 0 2 0 ad SN do gq oo Q4 UE eo o of uS Oe NU AP WP Beta law The law Beta represents the probability so that at least one material among N under test survives until time T It is also used to model Bayesian probabilities 2 3 Principle of the Monte Carlo simulation Monte Carlo simulation is a method of calculation based on random pulling Demonstration How to measure the surface of a figure drawn on the blackboard whose surface 1s known 1 Organize a chalk brawl in the classroom 2 Count the chalk impacts on the figure and on the whole of blackboard 3 Multiply the surface of the blackboard by the relationship between the first value and the second The precision of calculation will be of as much better than the brawl will be long and the participants bad sights Surface of the blackboard 4 m 1 5 m 6
52. w the user to build its simulation recursive model the tool offers random parametric functions to simulate various laws of probability on the spreadsheet macro functions These functions start with L_ followed by 3 first letters of the probability law and corresponding 5 arguments in brackets separated by a comma as in the following example L Wei 2 500 100 972 035706 3l The significance of the arguments of these functions is given in the following table law Code Argument 1 Argument 2 Argument 3 Argument 4 Argument 5 BEA Je N P M Mae BINOMIAL BIN Probabiiy Nootess Mn ma ERLANG ERL Lambda K Mn Me EXPONENTIAL EXP lamxa Mn Ma GAMMA GAM Lambda Bea Mn Ma GEOMETRICAL GEO Probabiity Mn Ma GuwBEL GUM a position b scale Mn ma HYPERGEOMETRIC HYP Nogood Nb ottests Nbwong Mn Max LOGNORMAL LOG Average S deviaton Max NORMAL NOR Average S deviaion Mn Ma PAREO Pan K Mnvhe Mn Ma wo Mn Ma PoSSON POL m o Mn Mae TRIANGULAR TRI Probable Mn Me UNIFORM UN ina By way of illustration the examples of recursive models presented hereafter are proposed in the on line help a Monitoring mechanism of liquid level in a tank hybrid system This mechanism of control all
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