Chapter-06-Slides

SimulationwithArena,3rded.Chapter6–Stat.OutputAnalysisTerminatingSimulationsSlide1of29StatisticalAnalysisofOutputfromTerminatingSimulationsChapter6LastrevisionJune8,2003SimulationwithArena,3rded.Chapter6–Stat.OutputAnalysisTerminatingSimulationsSlide2of29WhatWe’llDo...•Timeframeofsimulations•Strategyfordatacollectionandanalysis•Confidenceintervals•Comparingtwoalternatives•ComparingmanyalternativesviatheArenaProcessAnalyzer(PAN)•SearchingforanoptimalalternativewithOptQuestSimulationwithArena,3rded.Chapter6–Stat.OutputAnalysisTerminatingSimulationsSlide3of29Introduction•Randominputleadstorandomoutput(RIRO)•Runasimulation(once)—whatdoesitmean?Wasthisrun“typical”ornot?Variabilityfromruntorun(ofthesamemodel)?•NeedstatisticalanalysisofoutputdataFromasinglemodelconfigurationComparetwoormoredifferentconfigurationsSearchforanoptimalconfiguration•StatisticalanalysisofoutputisoftenignoredThisisabigmistake–noideaofprecisionofresultsNothardortime-consumingtodothis–itjusttakesalittleplanningandthought,thensome(cheap)computertimeSimulationwithArena,3rded.Chapter6–Stat.OutputAnalysisTerminatingSimulationsSlide4of29TimeFrameofSimulations•Terminating:Specificstarting,stoppingconditionsRunlengthwillbewell-defined(andfinite)•Steady-state:Long-run(technicallyforever)Theoretically,initialconditionsdon’tmatter(butpracticallytheyusuallydo)Notclearhowtoterminateasimulationrun•Thisisreallyaquestionofintentofthestudy•Hasmajorimpactonhowoutputanalysisisdone•Sometimesit’snotclearwhichisappropriate•Here:Terminating(steady-stateinSection7.2)SimulationwithArena,3rded.Chapter6–Stat.OutputAnalysisTerminatingSimulationsSlide5of29StrategyforDataCollectionandAnalysis•Forterminatingcase,makeIIDreplicationsRunSetupReplicationParameters:NumberofReplicationsfieldCheckbothboxesforInitializeBetweenReplications•Separateresultsforeachreplication–CategorybyReplicationreportModel5-2;DailyProfit,DailyLateWaitJobs;10replicationsSimulationwithArena,3rded.Chapter6–Stat.OutputAnalysisTerminatingSimulationsSlide6of29StrategyforDataCollectionandAnalysis(cont’d.)•CategoryOverviewreportwillhavesomestatistical-analysisresultsoftheoutputacrossthereplications•Howmanyreplications?Trialanderror(now)Approximatenumberforacceptableprecision(below)Sequentialsampling(Chapter12)•TurnoffanimationaltogetherformaxspeedRunRunControlBatchRun(NoAnimation)SimulationwithArena,3rded.Chapter6–Stat.OutputAnalysisTerminatingSimulationsSlide7of29ConfidenceIntervalsforTerminatingSystems•UsingformulasinChapter2,viewingthecross-replicationsummaryoutputsasthebasicdata:•Possiblymostusefulpart–95%confidenceintervalonexpectedvalues•Thisinformation(exceptstandarddeviation)isinCategoryOverviewreportIf1replicationspecified,Arenausescross-replicationdataasaboveOtherconfidencelevels,graphics–OutputAnalyzerSimulationwithArena,3rded.Chapter6–Stat.OutputAnalysisTerminatingSimulationsSlide8of29HalfWidthandNumberofReplications•Prefersmallerconfidenceintervals—precision•Notation:•Confidenceinterval:•Half-width=•Can’tcontroltors•Mustincreasen—howmuch?Wantthistobe“small,”sayhwherehisprespecifiedSimulationwithArena,3rded.Chapter6–Stat.OutputAnalysisTerminatingSimulationsSlide9of29HalfWidthandNumberofReplications(cont’d.)•Sethalf-width=h,solvefor•Notreallysolvedforn(t,sdependonn)•Approximation:Replacetbyz,correspondingnormalcriticalvaluePretendthatcurrentswillholdforlargersamplesGet•Easierbutdifferentapproximation:s=samplestandarddeviationfrom“initial”numbern0ofreplicationsh0=halfwidthfrom“initial”numbern0ofreplicationsngrowsquadraticallyashdecreasesSimulationwithArena,3rded.Chapter6–Stat.OutputAnalysisTerminatingSimulationsSlide10of29HalfWidthandNumberofReplications(cont’d.)•ApplicationtoautomotiverepairshopFrominitial10replications,95%half-widthonDailyProfitwas±$50.20...let’sgetthisdownto±$20orlessFirstformula:n1.962(70.172/202)=47.3,so48Secondformula:n10(50.202/202)=63.0,so63ModifiedModel5-2intoModel6-1–CheckedRunRunControlBatchRun(NoAnimation)forspeed–InRunSetupReplicationParameters,changedNumberofReplicationsto100(conservativebasedonabove)Got492.63±13.81,satisfyingcriterionSimulationwithArena,3rded.Chapter6–Stat.OutputAnalysisTerminatingSimulationsSlide11of29InterpretationofConfidenceIntervals•Intervalwithrandom(data-dependent)endpointsthat’ssupposedtohavestatedprobabilityofcontaining,orcovering,theexpectedvalued“Target”expectedvalueisafixed,butunknown,numberExpectedvalue=averageofinfinitenumberofreplications•Notanintervalthatcontains,say,95%ofthedataThat’sapredictioninterval…usefultoo,butdifferent•Usualformulasassumenormally-distributeddataNevertrueinsimulationMightbeapproximatelytrueifoutputisanaverage,ratherthananextremeCentrallimittheoremRobustness,coverage,precision–seebook(Model6-2)SimulationwithArena,3rded.Chapter6–Stat.OutputAnalysisTerminatingSimulationsSlide12of29ComparingTwoAlternatives•Usuallycomparealternativesystemscenarios,configurations,layouts,sensitivityanalysisFornow,justtwoalternatives...morelater•Model6-3Model6-1,butaddfileDailyProfit