AutoStat: Output Statistical Analysis for AutoMod Users
Contents
1. 3 Design of Experiments Setup DOE runs and graph and print DOE results 4 Graphs Plot of responses versus a factor Confidence interval plot of response for each configuration 4 STATISTICAL PROCEDURES IN AUTOSTAT In this section we describe the statistical capabilities of AutoStat These are divided between Warm up Determination in Section 4 1 and the analyses in Sections 4 2 4 5 The types of analyses offered include confidence intervals a 2 design of experiments and a ranking and selection procedure called Select the Best For more background on statistical methods in simulation see Banks Carson and Nelson 1996 and Law and Kelton 1991 4 1 Warm up Determination If you are interested in the steady state behavior of a system and not the warm up or initial transient caused by starting the simulation in an empty and idle condition or some other state not representative of steady state then you need to determine the length of the warm up or initial transient phase After determining a reasonable AutoStat TM Output Statistical Analysis for AutoMod TM Users 653 length for the warm up period you will run the simulation for a reasonably long period after the warm up phase so that system performance statistics responses can be collected over a period that is close to steady state conditions It is recommended that the steady state phase be at least twice as long as the warm up period since the warm2. A confidence interval for the difference in response between two scenarios is used to make a judgment regarding whether and how much of the observed difference is due to systematic differences in the two scenarios versus being due to mere random variation or noise To compute a confidence interval for a single scenario AutoStat computes the overall average response over all replications computes the sample standard deviation of the responses and the standard error of the overall average response Then it computes the confidence interval at the desired level of confidence usually 95 The confidence interval is an interval around the overall average response value that estimates uncertainty in the estimate of mean response it provides 654 Carson IT an estimate of the amount of variation in the overall sample average response due to statistical variation in the inputs for the particular runlength used A confidence interval should be used only when the response of interest is an average it should not be used for maximums or minimums This is because of the Statistical theory normality theory and the Central Limit Theorem on which the computations are based In fact AutoStat will not compute confidence intervals for statistics of type minimum or maximum Confidence intervals are perhaps more useful when comparing the response of two or more scenarios Suppose two alternative system designs A and B of a widget production faci
3. This initial sample is used to provide preliminary sample means and sample variances and to determine the number of additional samples needed to select the best subset with the specified probability of correct selection AutoStat TM Output Statistical Analysis for AutoMod TM Users 655 Note that P and d can be selected after the first stage of sampling the advantage of this is that AutoStat computes and displays the number of additional samples needed for a specified m P and d In general the final sample size N required for each configuration i gets larger as subset size m or indifference amount d decreases or as probability of correct selection P increases It is recommended that P be set at 95 and m and or d be made larger if the required sample size is too large for the available computer time Theoretically the Select the Best procedure could be used in a factorial experiment to automatically find the combination of factor values that results in an optimum response But in practice with even a moderate number of factors and factor values the procedure may require such a large number of replications as to exceed available computer time Therefore it is recommended that as many factors as possible be eliminated and set at some appropriate constant value by using either the Design of Experiments or multiple comparisons or perhaps Select the Best with a moderately large subset size Then Select the Best can be used
4. model s correctness Usually after modeling errors have been fixed and the model has been satisfactorily verified you should delete all runs made for verification and debugging purposes After all the model has probably changed during this period to fix errors and experimentation should be done with the final verified model The main purpose of using AutoStat in these early phases of a project before experimentation begins is as a quick test that a model runs to completion and that the outputs responses are reasonable over a wide range of possible inputs This provides much more robust testing over a wider range of conditions than can be achieved by making one run at a time manually 6 AUTOSTAT AND EXPERIMENTATION AutoStat was designed to provide a set of basic statistical procedures to assist during the experimentation phase of a project The data management and scenario management capabilities allow you to have more time to concentrate on the analysis itself instead of the tedious details of setting up runs and keeping track of all the output files 656 Carson IT The main purpose of the statistical procedures in AutoStat is to allow you to conclude with reasonable confidence that observed differences in response between two or more system designs or scenarios are due to a true systematic difference and not merely due to random noise When a model has one or more input variables defined as a statistical distribution say
5. up period is usually related to the maximum length of time it takes for parts to get through the system Having a warm up period that is too short failing to load the system to a state representative of steady state or failing to run the steady state phase long enough could result in performance statistics that are biased low due to the empty and idle initial state at time zero and that are not good estimates of the system s steady state behavior For warm up determination you should make a long run of one or more scenarios breaking the run into a large number of short snaps As a rule of thumb we recommend 100 snaps In AutoMod a snap is a reporting period standard output reports are written to a file at the end of each snap statistical accumulators are reset and the simulation continues If you tell AutoStat to make 100 snaps for warm up determination you will have a plot based on 100 response values one response value for each snap period You should verify that all parts of the system become loaded and process a reasonable number of loads during the specified runlength To determine whether it is reasonable to assume that the model has reached a steady state you should examine all key responses and how fast or whether they are converging to a steady state In addition you may want to define a number of special responses for detecting that all subsystems or all entity types have been successfully loaded For example you m
6. Proceedings of the 1997 Winter Simulation Conference ed S Andradottir K J Healy D H Withers and B L Nelson AUTOSTAT OUTPUT STATISTICAL ANALYSIS FOR AUTOMOD USERS John S Carson II AutoSimulations 1827 Powers Ferry Road Bldg 17 Suite 100 Atlanta Georgia 30339 U S A ABSTRACT AutoStat is an extension package for AutoMod and AutoSched models that provides complete support for simulation model experimentation and statistical analysis of outputs Within a menu driven point and click environment AutoStat provides assistance for setting up runs automated execution of runs and consolidation of outputs across replications and scenarios AutoStat automatically sets random number seeds to achieve statistically independent replications it also sets factor levels input parameters to realize desired scenarios without having to modify the underlying model AutoStat has a number of advanced features such as datafile factors responses or performance measures read from custom user output files and user defined combination responses linear combinations of other responses AutoStat offers several statistical methods including confidence intervals a ranking and selection procedure design of experiments and warm up determination Outputs can be displayed and printed in tabular and graphical formats and exported to spreadsheet and other analysis software AutoStat saves simulation modelers considerable time
7. and automates the effort of setting up and making runs managing the input and output files consolidating results and conducting analyses 1 INTRODUCTION The experimentation phase of simulation modeling and analysis is critical to the success of any simulation modeling project AutoStat provides assistance for all parts of the experimentation phase including e Setting up model runs e File management for the model s input and output files e Defining the desired scenarios to be run e Automatic execution of desired scenarios including control of random number streams 649 setting of factor levels input parameters and error tracking e Consolidation of outputs across scenarios and across statistical replications e Statistical calculations across replications including sample means and standard deviations e Statistical methods including Confidence intervals A ranking and selection procedure Design of experiments Warm up determination e Tabular and graphical display and printing of results e Export of tabular outputs to spreadsheets and other analysis software AutoStat works with both AutoMod and AutoSched models AutoMod is a general purpose simulation package with 3 D animation that provides pre programmed material handling simulators for conveyors and vehicle systems and special support for manufacturing systems AutoSched is a simulation based finite capacity production scheduling tool AutoStat provides all the tools
8. ay want to define responses for waiting times at the end of any product routing or throughput by product type to be sure that the whole system is loaded or that low volume or slow moving product has reached a steady state There is no known reliable method for automatically determining by a statistical or mathematical calculation when or whether a model has reached steady state The best methods are graphical and depend upon your judgment and your knowledge of the actual system To assist in determining the length of the warm up period AutoStat provides a moving average plot of any selected response over the snaps To reduce random fluctuations or noise the plot is averaged in two ways across replications and within replications The across replication averaging is automatic The within replication average is the moving average plot defined by a user adjustable window size A moving average is the average over several adjacent snaps of the response value for those snaps The number of adjacent snaps used to compute the moving average is called the window size The purpose of the moving average is to smooth the plot in order to detect the underlying trend or low frequency fluctuations over time by dampening the random noise or high frequency fluctuations Having a large number of short snaps makes the plots more meaningful easier to interpret and also allows for more flexibility in choosing a window size For example if you reque
9. d statistical calculations and with a few clicks of the mouse presents the statistical results in tabular and graphical formats ACKNOWLEDGMENTS This paper is an updated and modified version of a paper of the same name by the same author that appeared in the Proceedings of the 1996 Winter Simulation Conference John M Charnes Douglas M Morrice Daniel T Brunner James J Swain eds pages 492 499 REFERENCES AutoStat User s Guide AutoMod User s Manual Volume IT 1996 Bountiful UT AutoSimulations Banks J J S Carson and B L Nelson 1996 Discrete Event System Simulation Second Edition Upper Saddle River NJ Prentice Hall Carson J S 1996 AutoStat Output Statistical Analysis for AutoMod Users In Proceedings of the 1996 Winter Simulation Conference ed John M Charnes Douglas M Morrice Daniel T Brunner James J Swain 492 499 San Diego CA The Society for Computer Simulation Law A M and W D Kelton 1991 Simulation Modeling and Analysis Second Edition New York McGraw Hill AUTHOR BIOGRAPHY JOHN S CARSON is the Regional Consulting Manager for the Atlanta office of AutoSimulations With ASI since 1994 he has over 20 years experience in simulation in a wide range of application areas including manufacturing distribution warehousing and material handling transportation and rapid transit systems port operations and shipping and medical health care systems His current interests cente
10. ect the runs to compare choose the type of analysis or graphical comparison and AutoStat will extract the relevant outputs do the statistical analysis and display the comparative results automatically AutoStat can compare alternatives on the basis of any standard AutoMod output or any user computed output written to a custom output report Responses can be added after runs have been completed and analyses conducted on these responses without having to re run the model AutoStat makes it relatively simple to setup and run a large number of comparative simulations With a few selections with the mouse you can get results comparing the model s performance measures across any number of alternative scenarios Results can be displayed in graphical and tabular form In fact without using the statistical capabilities at all AutoStat can save you a tremendous amount of time during the debugging and verification phases of modeling and thus help to make your model more robust In addition when setting up and making a set of runs for comparing alternatives AutoStat can save you a tremendous amount of time compared to using batch files and manually managing all of the input and output files The remainder of this paper is organized as follows Section 2 covers the basic concepts for setting up runs in AutoStat namely responses factors configurations and sample types Section 3 explains the menu system Section 4 covers the statistical proced
11. ection procedures presented in Law and Kelton 1991 The goal is to select the best system defined as the one with the minimum or maximum value of some specified response from among k systems For example the best system might be the one with maximum throughput or minimum average time in system per part produced The procedure can select either the single best system or a subset containing the best system The subset size is designated by m For m 1 the single best system is desired For m gt 1 the procedure will select a subset of size m containing the best system Besides specifying k and m a user specifies the minimum probability of correct selection P and an indifference amount d Typically P 0 95 and the goal is P CS Prob Correct Selection P The choice of indifference amount d depends on engineering or practical considerations If the response of a system is very close to the response of the best system then we do not care which of the two systems is chosen as best More precisely if the two system responses are within d then we are indifferent to which one is chosen as best With this setup we are guaranteed that P CS gt P where correct selection is defined as the best or any system within the indifference amount of the best The ranking and selection procedure in AutoStat is a two stage procedure First an initial sample is taken of at least 5 runs of each configuration being compared
12. for example a time to failure that is exponentially distributed with mean of 6 hours then random noise in the responses is unavoidable Each independent replication uses a different stream of random numbers the result being observed variation in the output responses If there is a difference in the response of two system designs or scenarios is it a true systematic difference or merely noise The statistical procedures built into AutoStat can assist in making a sound judgment Since AutoStat saves the standard AutoMod output report and all designated custom reports in compressed form to minimize disk space usage you can add a new response after making the simulation runs This comes in especially handy when your boss or customer requests a new or different measure of system performance it avoids the necessity of repeating runs previously made 7 SUMMARY As with any analytic tool it s up to you to interpret the simulation results properly and determine the practical significance of the factors on the responses To leave more time for analysis AutoStat can save you a tremendous amount of time by making it easier to setup and make any desired number of test runs and experimental runs AutoStat will automatically save all the desired outputs and present them to you with a mouse click in both tabular and graphical formats For Statistical analysis AutoStat finds the desired outputs across any number of scenarios does all the require
13. lity were simulated for 4 replications and average widget time in system was compared Suppose further that AutoStat reports a 95 confidence interval on the difference in time in system between systems A and B as 3 2 3 8 hours or 0 8 to 7 0 hours Since the interval contains zero and thus overlaps both negative and positive ranges no conclusion can be drawn as to whether system A or B is better at least on a statistical basis However if a 4 hour improvement for widget time in system was of no practical importance it can be concluded that neither system is better than the other On the other hand if a 2 hour difference was of importance then more replications would be needed to reduce the width of the confidence interval so that a more precise estimate could be obtained With a sufficient number of replications the confidence interval should lie entirely to the left or entirely to the right of the value 2 in which case strong conclusions can be drawn If a tighter estimate of average difference were desired how many more replications would be needed In general to decrease the confidence interval width by half it is necessary to make 4 times the original number of runs For example for the widget example with 4 runs it would take 12 more runs for a total of 16 to get a confidence interval of roughly half the original width that is of roughly 3 8 2 1 9 hours in width 4 3 Design of Experiments One method for de
14. mulations with an initialization phase AutoStat can assist in determining the appropriate warm up period as described in Section 4 1 For a terminating non steady state simulation you simply define the desired runlength and a zero length warm up period 2 4 Setups To setup the sample runs for a configuration you define the value or range of values for each variable factor You can setup runs one at a time by specifying values for each variable factor in a configuration or you can setup multiple runs at once by defining the set of values for each factor and have AutoStat generate all combinations of factor values Finally you define the desired number of statistical replications with three being the minimum recommended number Each statistical replication of a scenario uses the same factor values but uses a unique stream of random numbers to guarantee statistical independence and random sampling as required by most statistical methods 2 5 Making Runs After defining factors and responses configurations and sample types and setting up the desired sample runs you make the model runs by clicking on the Run menu and selecting Do all runs AutoStat will automatically make the requested number of independent replications of all the scenarios that you have set up For example suppose that in a model of a production line the following variables are the experimental factors with factor values as given Number of Packing Machi
15. n the screen it will tell you whether the run completed the requested runlength or stopped with a modeling error Of course your model may also print messages to the message window perhaps reporting some logical error detected during the run Using the Display Samples menu item on the Sample menu you can display a table of all responses over all runs A quick visual scan of this table will usually indicate whether the responses are consistent within a scenario For example looking at throughput for the whole system and key subsystems will tell you whether the model has a lock up condition indicating a modeling error The purpose here is not a detailed analysis but rather to incorporate model verification into model development in an ongoing fashion and to provide more robust model testing by simulating over a wide range of factor settings If a run ends with an error or some unexpected output you can use AutoStat to easily repeat that particular run in normal interactive mode to find the cause of the problem You may use the debugger watch the animation or use any other debugging technique Choose Repeat Run on the Runs menu select the run you want to repeat and AutoStat will automatically set the factor values and the random number seeds so that you can repeat the previously made run After finding suspected errors and modifying the model to fix them you can again use AutoStat to repeat the previous run in order to verify the
16. nes 3 4 or 5 Number of Operators per Coloring Machine 1 operator per 1 machine 1 operator per 2 machines Production Schedule a datafile factor SCHED 1 DAT SCHED2 DAT AutoStat will automatically make the runs for each requested combination of factor values and save the standard AutoMod output report and all custom reports that contain responses In this example for one replication per scenario and using all combinations of factor values each set of runs amounts to 3 x 2 x 2 12 runs With 3 replications AutoStat would make 36 runs Multiple replications are needed by most statistical procedures 3 MENUS AND MECHANICS With Version 8 0 and higher AutoStat and other AutoSimulations products are true Windows products for the PC and are based on the Motif graphical user interface on UNIX platforms To set up and make runs you use the Model Responses Factors Configurations Samples and Runs menus The Model menu is for opening models and saving AutoStat default data With these menus you setup all AutoStat experiments and get many of the benefits of using AutoStat in terms of data and scenario management The other menus cover the statistical and display capabilities 1 Warm up Determination Setup warm up runs and display Welch moving average plots of responses over time 2 Confidence Intervals Single and comparison intervals the select the best ranking and selection procedure
17. o allows user responses and combination responses Any output statistic printed to a custom output report is called a user response AutoStat can be taught to read a custom output report and find the desired output to be used as a response To achieve this the custom output report must contain a snap separator that is a unique string that identifies the AutoStat TM Output Statistical Analysis for AutoMod TM Users 651 beginning of the custom report for the warm up period if any and the beginning of the report for the steady state portion of the run For models without a warm up period the snap separator can be any string at the top of the output file The custom report also must contain one or two unique strings of characters each usually a header or title before the desired statistic either on the same or a preceding line as the statistic AutoStat is then told to look on the same line as or a specified number of lines after the unique character string and to read a specified column from that line counting columns starting at 0 You must also tell AutoStat whether the statistic is an average a total such as counting the occurrences of some event a minimum or a maximum so that AutoStat can handle any subsequent analyses properly Identification of AutoSched responses has been automated even further Standard AutoSched output files are displayed in an edit table format similar to a spreadsheet with rows and column
18. r on the simulation of transportation systems train systems bulk and liquid processing and software for simulation output analysis He has been an independent simulation consultant and has taught at Georgia Tech the University of Florida and the University of Wisconsin Madison He is the co author of two textbooks including the widely used Discrete Event System Simulation Second Edition 1996 He holds a Ph D in Industrial Engineering and Operations Research from the University of Wisconsin Madison and is a member of IIE and INFORMS
19. s After you identify the factors you want to vary define the scenarios of interest and specify the number of replications desired AutoStat will automatically make all the runs for all desired scenarios and archive the outputs for later analysis and display of comparative results For each run AutoStat automatically sets the seeds for all random number streams and sets user specified values for factors including data file factors without modification to the underlying model In support of debugging and verification AutoStat allows previous runs to be repeated interactively so that suspicious outputs can be investigated and the model verified and errors corrected When repeating a run for debugging purposes AutoStat automatically duplicates all previous settings including random number seeds and factor values Models with errors can be corrected and previous runs re made for verification purposes If your model has probabilistic or statistical components such as random arrivals or random processing times then you need AutoStat for conducting a Statistical analysis to determine whether observed differences in a response between two scenarios or two system alternatives are real differences or are merely due to random fluctuations If your model is deterministic then AutoStat can still save you considerable time and effort in setting up and making runs across numerous scenarios After AutoStat makes all the runs you request you sel
20. s Clicking with the mouse on a desired element identifies the output in that row and column as a response Combination responses are new responses defined as linear combinations of other responses This allows responses such as cost functions or averages to be computed by AutoStat without changing the model in any way For each run made AutoStat saves the complete AutoMod report plus all custom reports requested to an archive in a compressed format to minimize usage of hard disk space Because of the archiving of all outputs additional responses can be defined after a set of runs have been completed without having to re run the model and additional analyses conducted 2 2 Factors A factor is a model input parameter that can be varied during experimentation Usually a set of factors set to particular values defines a scenario or alternative system design of interest Examples of factors include the number of workers product flow machine speeds production schedules and operating rules order files conveyor speeds and vehicle performance specifications speeds accelerations In an AutoMod model the following items can be factors Capacity of a resource counter block or any other built in entity Speed or other performance parameter of a vehicle in an AGVS ASRS Bridge Crane Power amp Free or other vehicle system Capacity of a vehicle number of loads that can be transported Speed of a conveyor sec
21. st 100 snaps and a window size of 1 the plot will consist of 100 response values If you request a window size of 3 then snaps 1 3 are averaged snaps 2 4 are averaged and snaps 98 100 are averaged resulting in 98 values to be plotted To determine a reasonable warm up period you must use not only the moving average plots with a suitably chosen window size but also your knowledge that all areas of the system have reached a reasonable loading It should be kept in mind that some configurations may not have steady state usually indicated by a response value that continues to rise in value the longer the model is simulated The AutoStat moving average plot can assist in determining whether a steady state is reached at all After you have determined the warm up period you setup a sample type with the warm up and steady state runlengths desired and AutoStat will automatically ignore the responses over the warm up and use responses over the steady state for all analyses 4 2 Confidence Intervals A confidence interval for a single scenario is used to estimate long run mean value of a response It measures the effect on the estimate of mean response due to inherent statistical variation in the model As more replications are made the width of the confidence interval decreases indicating greater certainty in the estimate in a Statistical sense A short confidence interval does not of course say anything about a model s validity
22. termining which factors have a statistically significant effect upon any response is to apply AutoStat s design of experiments Statistical significance for a factor means that with high confidence the observed variation in mean response as the factor is varied from a low to a high setting is more than can be accounted for by mere random variation that is the observed variation of the response is larger than what would be expected due to the random variation alone Thus the factor is judged to have a significant effect on the response value With this procedure you can quickly eliminate from further experimentation many factors that have little or no effect on the important system performance measures and use future computer and analysis time more profitably by concentrating on the factors most likely to have a large effect on system response AutoStat offers the so called 2 design each factor is allowed two values a low and a high setting AutoStat offers the full factorial design requiring all combinations of factor levels to be simulated For example for k 5 factors a total of 2 32 runs are needed for each replicate of a full factorial design AutoStat also offers several lower resolution designs allowing a trade off between number of runs and the possible inferences that can be drawn reliably 4 4 Select the Best AutoStat also offers a Select the Best ranking and selection procedure one of the subset sel
23. tion Size of a load important for conveyor models Initial value of a variable External input data file In addition to these factors a special type of factor is available for AutoSched models All AutoSched models are driven by a standard set of input tables defined through a spreadsheet like user interface Examples include Station Routing and Calendar files When defining an AutoSched factor AutoStat displays the actual input table and you may select one or more cells as factors This means that you desire to change the values in this group of cells during experimentation In addition to cells rows to be modified or added can be defined as AutoSched factors When any of these parameters is designated as a factor and assigned values AutoStat will automatically override their value in the model called the base value without any more effort on your part than choosing the factor and typing the desired factor values Operating logic can be made a factor by using an input variable as a flag for example to indicate which set of operating rules to use and having the model select which rules to use based on the variable s value In this way alternative operating rules or logic can be compared against each other As mentioned an external input data file can be defined as a factor Examples of potential data file factors include production schedule files product routing files order files machine processing times and do
24. ures available in AutoStat Section 5 discusses the use of AutoStat during model debugging and verification and Section 6 discusses it use during experimentation Section 7 provides a summary 2 BASIC CONCEPTS To use AutoStat to make runs for the purpose of experimentation or model verification you begin by defining responses factors configurations and sample types First you define the responses or measures of system performance second you define the factors or input parameters that will be varied to generate alternative scenarios or system designs to be compared A set of factors is grouped into a configuration or experimental framework to define the desired scenarios to be simulated For each factor in a configuration you then define the desired value or range of values and AutoStat automatically generates the requested runs You also must specify the sample type namely the warm up period and runlength plus the number of statistical replications Then AutoStat takes over makes all requested runs and archives the results for later analysis This section discusses these basic concepts 2 1 Responses A response is a model output usually a measure of system performance For example typical responses include machine or worker utilization average and maximum queue size and throughput A response can be any output statistic captured by AutoMod or AutoSched and printed to any of the standard output reports AutoStat als
25. with a small number of the most significant factors to determine the optimum combination of factor values 4 5 Graphical Displays AutoStat provides graphical displays of one or more responses versus a factor and plots of confidence intervals for a selected set of configurations In addition the results of the Design of Experiments can be displayed graphically namely the confidence intervals for the main and interaction effects 5 USING AUTOSTAT DURING MODEL TESTING AND VERIFICATION Even before using its statistical capabilities AutoStat can be of great assistance during model testing and verification In brief AutoStat provides a quick way to setup and run a large number of tests overnight or over a weekend and a quick and convenient way to view the resulting outputs for face validity Key parameters can be varied easily by selecting them as factors In fact in a brief 10 to 15 minutes for setting up runs almost any number of test runs can be setup and started For verification purposes you should make at least 3 statistical replications and run as wide a range of scenarios as possible given the available computer time When you return to view the results most likely AutoStat will have finished all the runs If not simply click on the Cancel button to abort the remaining runs Completed runs will be saved and canceled runs can be completed at a later time if desired For each run made the usual AutoMod message window is o
26. wntime data To use a datafile factor first you create two or more alternative input files Then by point and click you tell AutoStat that the input file is a variable factor and specify the alternative file names For example suppose a model of a distribution center reads a file of daily orders called order d You obtain samples of order files for 5 different days over the past year calling them order 1 order 2 and order 5 You tell AutoStat that order d is a datafile factor and specify the names of the alternate order files When such a file is used as a factor AutoStat automatically copies the alternate files to the filename hard coded in the model saving the original and restoring it after all runs are completed No changes to the model itself are required 2 3 Configurations and Sample Types Defining configurations and sample types is the next step in setting up experimental runs AutoStat uses the concept of a configuration to designate a set of factors to be varied for a particular analysis Other factors if any are given a constant value either the value hard coded in the model or any other desired value A 652 Carson IT configuration thus provides an experimental framework for a group of experiments Next you define the sample type or run conditions For example for a particular model it might be appropriate to have an 8 hour warm up period and a 40 hour run For steady state si
27. you need for setting up runs and conducting a proper statistical analysis in an easy to use point and click menu driven environment AutoStat provides warm up determination for steady state analyses single and multiple comparison confidence intervals for the estimation and comparison of mean system performance measures the design of experiments to determine the significant factors and a ranking and selection procedure select the best for finding the best system Statistical results can be displayed in both tabular and graphical formats Responses or system performance measures that can be analyzed include all those in the standard AutoMod output report plus responses printed to custom output reports In addition you can define a response as a linear combination of other previously defined responses without modifying the underlying model 650 Carson II In support of experimentation and analysis AutoStat provides automated set up and execution of model runs file management and consolidation of outputs across runs You define the factors or input parameters that you want to vary Each set of factor values defines a different scenario or system alternative of interest Possible factors include any standard AutoMod input parameter such as number of vehicles or operators conveyor speed or vehicle speed any user defined variable s initial value or any user input data file such as a production schedule or daily order
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