E a s t ern Medi t er r anean Uni v e r sity Depart m e n t of I nd u s tr i al Engin e er i ng

1. Eastern Mediterranean University DepartmentofIndustrialEngineering IENG461 Modelingand Simulation Systems Computer Lab 2nd session ARENA(InputAnalysis) Prepared by: Sam Mosallaeipour

2. DATACOLLECTIN ACTIVITIES Considermodelinga paintingworkstation where jobsarrive at random,wait in abufferuntilthe sprayeris available,and havingbeensprayed, leavethe workstation. Suppose thatthe spray nozzle can get clogged—aneventthatresults astoppageduringwhich the nozzle is cleaned replaced. in or

3. SIMULATIONMODELING Suppose thatyou areasked tosimulatethis paintingworkstation. Listthe required data to estimatethe expectedjob delay inthe bufferfor thissimplesystem

4. DATACOLLECTION Collection ofjobinterarrivaltimes. • – Clock timesare recordedon job arrivals and consecutivedifferencesarecomputed to form the requisitesequenceof jobinterarrivaltimes. Ifjobsarrive inbatches,thenthebatchsizesper arrival eventneed to berecordedtoo. Ifjobshavesufficientlydifferentarrival characteristics (dependingon theirtype),thentheanalystshould partition thetotalarrival streaminto substreamsof differenttypes,anddata collection(of interarrival timesand batchsizes)shouldbe carriedout separatelyfor eachtype. – –

5. DATACOLLECTION Collectionof paintingtimes. • –Theprocessingtimeisthetime it takestospraya job.Sincenozzlecleaningorreplacementis modeledseparately(seelater),thepaintingtime shouldexcludeanydowntime.

6. DATACOLLECTION Collectionof timesbetweennozzleclogging. • – Thisrandomprocessisalsoknownastimeto failure. Observethatthe nozzleclogging processtakes placeonlyduringpaintingperiods,andis suspendedwhilethesystemisidle.Thus,the observationsof theeffectivetime to failureshould becomputedasthetime intervalbetweentwo successivenozzlecloggingsminusthetotalidle time inthat interval (if any). –

7. DATACOLLECTION Collectionof nozzlecleaning/replacement • times. –Thisrandomprocessisalsoknownasdowntime orrepairtime. –Observationsshouldbecomputedasthetime interval fromfailure(stoppage)onsetto the time thecleaning/replacementoperationiscomplete.

8. DATACOLLECTION Suppose wecollected the followingsample data for repairtimes(nozzle cleaning/replacement timesfor paintingstationgiven above) and recordedthemin afile named as “repair.txt”:

9. SAMPLEDATA FOR REPAIRTIMES 12.9 20.9 30.0 17.0 11.0 10.3 10.9 21.0 22.8 10.8 20.5 22.2 14.3 13.3 28.6 19.4 18.9 16.7 12.7 19.5 27.7 26.6 27.4 21.7 27.5 18.0 27.0 21.3 25.9 10.3 19.4 25.5 29.9 24.0 26.9 27.4 11.9 28.5 18.1 11.9 13.5 29.1 18.8 13.7 22.5 11.5 24.2 23.1 22.4 15.1 10.9 17.2 17.8 29.7 20.7 22.5 13.2 19.9 15.0 22.9 13.7 22.4 25.3 15.5 27.1 14.1 25.6 15.8 13.8 19.0 24.1 10.9 19.8 18.1 22.0 28.3 10.9 18.5 21.0 23.2 22.2 10.7 15.0 23.2 25.2 24.0 22.4 13.2 16.6 27.9 10.9 15.6 17.6 28.4 16.8 27.1 22.1 16.5 25.7 18.9 Save as “repair.txt” than change fileextension as “.dst”

10. CHI-SQUARETESTforUniformDistribution(RepairData) Cellnumber CellInterval #ofObservations RelativeFrequencyTheoreticalProbability Why? 1 2 3 4 5 6 7 8 9 10 [10,12) [12,14) [14,16) [16,18) [18,20) [20,22) [22,24) [24,26) [26,28) [28,30) 13 9 8 9 12 8 13 10 10 8 0.13 0.09 0.08 0.09 0.12 0.08 0.13 0.10 0.10 0.08 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 2 0.10,7 12 k -s-1 = 10-2-1=7,α= 0.10 2 2  0.10,7 3.6 12 Cannot rejectthe nullhypothesis

11. ARENA INPUT ANALYZER Arena providesbuilt-indataanalysis facilities • via is to its Input Analyzer tool, whose mainobjective fit distributionstoa givensample. • Keepin mind thatArena providesbuilt-infacilities for fittingdistributions to independentempirical data,however,Arena does not provide anybuilt- in facility for fitting dependent (time series) random processes.

12. ARENA INPUT ANALYZER TheInputAnalyzeris accessible fromtheToolsmenuinthe Arena homescreen. Afteropeninganewinputdialogbox(byselectingtheNewoption theFile menuinthe InputAnalyzerwindow),rawinputdatacanbe in selectedfromtwosuboptionsintheDataFileoptionoftheFilemenu: 1.ExistingdatafilescanbeopenedviatheUseExistingoption. 2. New(synthetic)datafiles canbe createdusingtheGenerateNew optionasiidsamplesfromauser-prescribeddistribution. OncethesubsequentInputAnalyzerfileshavebeencreated,theycan beaccessedintheusualwayviatheOpenoptionintheFilemenu

13. ARENA INPUT ANALYZER TheArenaInputAnalyzerfunctionalityincludes fitting adistributionto sampledatain two ways: 1.Theusercanspecifyaparticularclassof distributionsandrequesttheInputAnalyzerto recommendassociatedparametersthatprovidethe fit. best 2.The usercanrequesttheInputAnalyzer to recommend boththeclassof distributions aswell asassociated parametersthatprovidethe bestfit.

14. ARENA INPUT Distribution Arenaname Arena parameters ANALYZER • • • • • • • • • • • • • • • • • Exponential Normal Triangular Uniform Erlang Beta Gamma Johnson Log-normal Poisson Weibull Continuous Discrete EXPO NORM TRIA UNIF ERLA BETA GAMM JOHN LOGN POIS WEIB CONT DISC Mean Mean,StdDev Min,Mode,Max Min,Max ExpoMean,k Beta,Alpha Beta,Alpha G,D,L,X LogMean,LogStdDev Mean Beta,Alpha P1, V1, ...a P1,V1,. .. aTheparametersP1, P2,...arecumulativeprobabilities. TabledisplaysthedistributionssupportedbyArenaandtheirassociatedparameters.

15. ARENA Whenyouopenthis file via“Use ExistingOption”, theInputAnalyzer automatically createsa histogram fromthesesample data,andprovides asummaryof, samplestatistics,as shown inthe figure. INPUT ANALYZER

16. ARENA INPUT ANALYZER The Optionsmenu inthe InputAnalyzermenubar allows theanalysttocustomizeahistogrambyspecifyingits numberofintervalsthroughtheParametersoptionandits Histogramoption’sdialogbox.Onceadistributionis fitted tothe data(seenextsection), the samemenualsoallows theanalysttochangetheparametervaluesofthefitted distribution. • • As mentioned above,either the usercanspecifya particulardistributionandrequesttheInputAnalyzerto recommendassociatedparametersforthisdistributonor usethe“bestfit”optiontodecidewhichdistributionto useforthesesampledata.

17. ARENA INPUT ANALYZER SpecifyingUniformDistribution

18. ARENA INPUT ANALYZER FitAllSummary: