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1、DesignofExperiments:TheD-OptimalApproachandItsImplementationAsaComputerAlgorithmFabianTriefenbach15thJanuary2008Bachelor'sThesisinInformationandCommunicationTechnology15ECTSSupervisoratUmU:J?urgenB?orstlerSupervisoratFH-SWF:ThomasStehlingExaminer:PerLindstr?om
2、UmeoaUniversityDepartmentofComputingScienceSE-90187UMEoASWEDENSouthWestphaliaUniversityofAppliedSciencesDepartmentofEngineeringandBusinessSciencesD-59872MESCHEDEGERMANYAbstractMotivation:Theuseofexperimentsinane?ectivewaytoanalyzeandoptimizeagivenprocessisapro
3、blemstatementwhichshouldbepaidmoreattentiontointheengineeringcommunity.Frequently,experimentsareˉrstperformedandthemeasureddataisanalyzedafterwards.Incontrasttothis,statisticalmethods,liketheconceptofDesignofExperiments,shouldbeusedtoplanexperimentaldesignsand
4、performsetsofwellselectedexperimentstogetthemostinformativecombinationoutofthegivenfac-tors.ProblemStatement:TheSwedishcompanyUmetricsABisdevelopingspecialsoftwaretoolswhichdealwiththisˉeldofstatisticalexperimentaldesign.InsidethesoftwareMODDEafeatureforthecre
5、ationofaspecialdesigntype,theD-optimalde-sign,isgiven.Theaimofthepresentthesisisthereimplementationofthisprogramunitwithimprovementsinthequalityofthegenerateddesignsandthecomputationalef-fort.Approach:D-optimaldesignsarebasedonacomputer-aidedexchangeprocedurew
6、hichcreatestheoptimalsetofexperiments.Anintensiveliteraturestudybringsforthsixdi?erentapproachestohandlethisexchangewithacomputeralgorithm.IndetailacomparisonandevaluationoftheFedorovprocedure,themodiˉedFedorovprocedure,theDETMAXalgorithm,thek-exchangealgorith
7、m,andthekl-exchangealgorithmisperformed.Basedonthis,anewalgorithm,themodiˉedkl-exchangealgorithm,isdevel-opedandusedfortheimplementationinC++.Results:Theoutcomeofthepresentthesisisanimplementationofthefourmostadvisablealgorithms.TheFedorovandnormalFedorovalgor
8、ithmgeneratethebestdesignsconsideringtheD-optimalityofthedesignsbutareverytime-consumingforbigdatasets.Asanalternativethek-exchangealgorithmandamodiˉedversionofthekl-exchangealgori
