DFSS-BB310-Full-Factorial-DOE.ppt

DesignforSixSigma FullFactorialDesignofExperimentsDFSSBB310FullFactorialDOE ppt Purpose DemonstratehowtogenerateafullfactorialdesignDemonstratehowtocreate analyzedesignsinMINITAB DemonstratehowtolookforfactorinteractionsDemonstratehowtoevaluateresidualsDemonstratehowtosetfactorsforprocessoptimization DetermineCustomers Y s Quality Price ProductDemand InitialProductPlatformkeyX s productvelocities MeasuretheX sandY s FindcriticalY f x relationships OptimizeY s criticalX s RMI WIP FGI SupplyChain SetcriticalX s kan bans CheckKeyY s Failuremodesandanalyses DFSSRoadmap SelecttheProperDOEDesign Theselecteddesignshouldalignwiththeobjectivesoftheexperimentandresourcecommitment OFAT OneFactorataTime FullFactorial withorwithoutreplication 2kFullFactorial2kFullFactorial centerpoints 2kFullFactorial blocking 2k nFractionalFactorialDesignsRSM ResponseSurfaceMethod Highercomplexitydesignsoffergreaterknowledgeatahigherprice ExperimentTypes Objective RSM ResponseSurfaceMethod Optimize Model ResolutionIIIFractionalFactorialDesignsFullFactorialDesignsResolutionVFractionalFactorialDesigns 2kFullFactorial Screen Few Many PIV s Less More KNOWLEDGE Less More COST 6 15 2 5 ExperimentalDesignConsiderations Review complexityvsvalue WhyLearnAboutFullFactorialDOE AFullFactorialDesignofExperimentwill ProvidethemostresponseinformationaboutFactormaineffectsFactorinteractionsWhenvalidated itwillallowaprocesstobeoptimized WhatisaFullFactorialDOE AfullfactorialDOEisaplannedsetoftestsontheresponsevariable s KPOVs withoneormoreinputs factors PIVs eachwithallcombinationsoflevelsevaluatedANOVAwillshowwhichfactorsaresignificantRegressionanalysiswillprovidethecoefficientsforthepredictionequations forthecasewhereallfactorshave2levels MeanStandarddeviationResidualanalysiswillshowthefitofthemodel Learningthemostfromasfewrunsaspossible Identifyingwhichfactorsaffectmean variation both orhavenoeffectOptimizingthefactorlevelsfordesiredresponseValidatingtheresultsthroughconfirmation FullFactorialDOEObjectives Istestingallcombinationspossible reasonableandpractical CombinationofFactorsandLevels 1 AprocesswhoseoutputYissuspectedofbeinginfluencedbythreeinputsA BandC TheSOPrangesontheinputsare A15through25 byincrementsof1B200through300 byincrementsof2C1or2ADOEisplannedtotestallcombinations Wemustmakeassumptionsabouttheresponseinordertomanagetheexperiment CombinationsofFactorsandLevels 2 Settingupamatrixforthefactorsatallpossibleprocesssettinglevelswillproduceareallylargenumberoftests ThepossiblelevelsforeachfactorareA 11B 51C 2Howmanycombinationsarethere 2x51x11 2x51x11 Thedesignbecomesmuchmoremanageable LinearResponseforFactorsatTwoLevels Theteamdecides fromprocessknowledge thatthetestconditionsofinterestwithintheoperatingrangeofthefactors inferencespace isasshownbelow A15 20and25 3 B200 225 250 275and300 5 C1and2 2 Thisisa3x5x2fullfactorialdesign Itconsistsofallcombinationsofthethreefactors TheThreeFactorFullFactorialDesign TherevisedexperimentconsistsofallpossiblecombinationsofA BandCateachofthechosensettings levels Totalruns 3x5x2 30 ClassExercise Whatisthetotalnumberofcombinationsforthefollowingdesigns 2x3x43x3x33x2x2x4x3x5 CreateaMINITABdesignfor A pressure10 12 14 16psiB temperature65 70 75degreesC materialvendorAcme World Wide 4x3x2Design CreatingaFullFactorialinMINITAB CreatingaFullFactorialinMINITAB CreatingaFullFactorialinMINITAB 1 SelectOptions 2 Un checkRandomizeruns forteachingpurposesonly 3 Select OK CreatingaFullFactorialinMINITAB CreatingaFullFactorialinMINITAB CreatingaFullFactorialinMINITAB ThisistheStandardorderfora4X3X2design TheStdOrderColumnshowstheorderoftherunsifthedesignisnotrandomizedTheRunOrdercolumnshowstheorderoftherunsifthedesignisrandomizedNote SincewedidnotchecktheRandomizeboxwhenwecreatedthedesign bothStdOrderandRunOrderarethesame ClassExercisePart1 Createbotharandomizedandnon randomizedMINITABdesign 1replicate forthefollowing Thefactorsandrespectivelevelsare FactorLEVELSCustomerTypeC IConsumerSystemLegacySAPWarehouseAtlantaDallasStLouisOvertimeHours0100Theresponseison timedeliveryBepreparedtodiscussyourresults Replication RepeatsandRandomization DesignforSixSigma ReplicatesandRepeats AReplicateis TotalrunofalltreatmentcombinationsUsuallyinrandomorderAllexperimentswillhaveonereplicateTworeplicatesaretwocompletesetsofexperimentrunsEachreplicateisanotherrepetitionoftheentireexperimentWhentherearetwoormorereplicates thecompletesetofrunsisgenerallyrandomized iftherandomizationisdoneonlyforthefirstreplicate andeachrunisrepeated2ormoretimes thesearecalledrepeatsStatisticallybestexperimentalscenario Multiplereplicatesincreasestatisticalpowerofexperiment MINITABDesignReplication MINITABhandlesreplicatingthedesigneasilyActualfactorlevelchangebetweenrunsisatthediscretionoftheexperimenterMINITABprovidestreatmentcombinationRandomizationorinformationneededispartofstrategyofexperiment ReplicationinMINITAB Step1 Createa2x3FullFactorialwithtwononrandomizedreplicates ToolBarMenu Stat DOE Factorial CreateFactorialDesign ReplicationinMINITAB Step2 ReplicationinMINITAB Step3 ClickFactors ReplicationinMINITAB Step3 ReplicationinMINITAB Step4 Skiptheotherdialogoptions Un checkrandomizeboxinOptions ReplicationinMINITAB Step5 FirstReplicate SecondReplicate ResponseYwouldbeplacedinC6 ReplicationinMINITAB forStep5 ResponseYwouldbeplacedinC6 Randomization TheExperimenter sInsurance Letsdiscussaplatingetchbath Theoutputofconcernisetchrate higherisbetter Someonewantstoevaluateifaddingastirrertothebathwillincreaseetchrate Wetellthesupervisortoevaluateetchrate20timesforbothstirreronandstirreroff Weareinahurryandtellhimthathehasonedaytodothetest Whatdoweget AvgOff 91 70AvgOn 74 50 Ifhigherisbetter Randomization TheExperimenter sInsurance Ran20withstirrer off then20withit on Randomization TheExperimenter sInsurance AvgOff 82 0AvgOn 88 6 Ifhigherisbetter Ran20 on 20 off withRandomization TheResults Whichtellsthetruthaboutthevalueofstirring Thedegradationofthebathoverthedayiscalleda lurkingvariable Whilethisonewouldhavebeeneasytopredict notalllurkingvariablesaresoobvious Randomizewheneverfeasible Assumptions DesignforSixSigma AssumptionsforAnalyzingFullFactorials FullFactorialsuseANOVAtoanalyzethedata Thus theassumptionsarethesameasforOne WayANOVA TheresidualsareIndependentNormallydistributedWithequalvarianceInaddition sinceFullFactorialshavemorethanonefactor wehaveanotherassumption Thefactorsareindependentofeachother Independence IndependentData Notrends patterns orclusteringMoststatisticalmodelingtechniquesassumethattheresidualsareindependent includingANOVAandregression ThevalueofapointshouldnothelppredictthevalueofthenextpointIndependentVariables NocorrelationMoststatisticalmodelingtechniquesassumethatthefactorsorpredictorvariablesareindependentofeachother includingANOVAandregression Independenceisacriticalassumption lackofindependence CanbiastheresultsofastudyCanresultinextremelyunstablepredictionmodels IssuesRelatedtoIndependence SamplingQuestionsMostproblemsrelatedtosampledatacomebacktothesamplingmethod Wassampledatacollectedrandomly Weresamplingtechniquesclearlyoutlined Doestheorderinwhichthedatawerecollectedmatter CorrelatedFactorsorPredictorsOrthogonaldesignsusedinDOEensureindependentfactors TestingIndependence IndependentDataorResidualsOrderisimportantRunchartorIChartofdataorresidualswillshowtrends patterns clustersThesechartshavetestsfortrendsandclustering usethemThedatashouldberandom withnorepeatedcyclesorlongtermtrendsIfthedataisrandomwithnotrends thenthedataisindependentandstableOrderisnotimportantIftrendsorpatternsaredetected ignorethem orderisnotimportant Example Duetocost wedidnotrandomizeourdesign wehopethatourdatawillshowastrongpatternasweranallofthetestsatonesettingbeforechangingtonewsetting Wehopethatonesettingwillshowanimprovement TestingIndependence IndependentVariablesorFactorsScatterplots ormatrixplots showrelationshipbetweenvariablesIfvariablesarecorrelated selectonethat IseasytomeasureHasthemostintuitiverelationshipwithY Normality Thevastmajorityofstatisticaltests ANOVAincluded aretheoreticallybasedupontheassumptionofnormalityNon normalityaffectsthecalculationsforp valuesandPower Powerdecreaseswithnon normaldata andp valuesarereportedasbeingsmallerthanactualThevastmajorityofstatisticaltests ANOVAincluded arealsoquiterobusttodeparturesfromnormality especiallyforlargesamplesTransformationscanoftenbeusedto normalize data Formoreinformationonthenormalityassumption refertothepaper NormalityAssumption intheSupportFiles IssuesWhenTestingforNormality 1 TesttheRightDataRemember theassumptioninANOVAisthattheresidualsarenormal thereforewetestthem notthedataSampleSizeHistogramsrequirelargesamples 50ormorerecommended ProbabilityPlotsdon trequireaslargeasampleTestsfornormalityrequire25ormoreobservations don thavemuchpowerunlessn 50AsaresultoftheCentralLimitTheorem mosthypothesistestsarerobusttonon normalitywhensamplesizen 20 Testingfornormalityalmostalwaysrequiresmoredatathanthestatisticalteststhatassumenormality IssuesWhenTestingforNormality 2 NatureofNon NormalityHeavilyskeweddataismoreofaconcernthannon normalsymmetricdataHeavilyskeweddataiseasiertofixwithatransformationLog Box CoxPowerTransformation SquareRoot Arcsine etc Non ParametricAlternatives DoesnotapplyforFullFactorials exceptthespecialcasewhentherearetwofactorsMostnon parametrictestsrequiresymmetricdata andarejustassensitivetoheavilyskeweddataastheparametrictestsAllnon parametrictestsarefarlesspowerfulthanthecorrespondingparametrictests unlesssamplesizeisverylarge inwhichcasetheparametrictestsareextremelyrobustanyway Ifdataisheavilyskewed itisbettertotryatransformationthananon parametricalternative StepsforTestingNormalityAssumption Step1 Testtherightdata for2k testtheresiduals Step2 GraphicalmethodsHistogramofresidualsNormalprobabilityplotofresidualsStep3 StatisticaltestsAnderson Darlingtest preferred Chi Squaregoodnessoffittest Alwaysusegraphicaltoolswhentheyareappropriate EqualVariances Statisticalmodelingtechniques includingANOVAandregression assumethattheresidualshaveequalvarianceUnequalvariancesaffectthecalculationsforp valuesandPower Powerdecreasesandreportedp valuesaresmallerthantheactualp valuesThevastmajorityofstatisticaltestsarealsoquiterobusttounequalvariances especiallywhensamplesizesareequalornearlyequal forANOVA thismeansthatthenumberofrunsforeachlevelofafactor orthenumberofrunsforeachcombinationoflevelsoftwoormorefactorsisthesame Transformationscanoftenbeusedtocorrecttheproblem Formoreinformationontheequalvarianceassumption refertothepaper EqualVarianceAssumption intheSupportFiles IssuesWhenTestingforEqualVariances SampleSizesTestsongroupeddata ANOVA areveryrobusttounequalvarianceswhenthesizesofthegroupsareequal ornearlyequalNon ParametricAlternativesDonotapplytoanalyzingfullfactorialsexceptthespecialcaseof2factorsMostnon parametrictestsrequirethatthedistributionshavethesameshape inotherwordstheyarealsosensitivetounequalvariancesAllnon parametrictestsarefarlesspowerfulthanthecorrespondingparametrictests unlesssamplesizeisverylarge Ifthevarianceincreasesasthemeanincreases itisbettertotryatransformationthananon parametricalternative StepsforTestingEqualVarianceAssumption Step1 Testtherightdata residuals Step2 DefinetherighttestEqualvariancesforallresiduals onegroupofdata Step3 GraphicalmethodsResidualsvs fitsStep4 StatisticaltestsFtestfor2variancesBartlett sandLevene stestsfor 2variances Alwaysusegraphicaltoolswhentheyareappropriate TheImportanceofOrthogonalDesigns Factorsaremathematicallyindependentwhenthecorrelationbetweenthemis0OnlytheresponseisafunctionofthefactorsAfactorisnotafunctionofanotherfactorFactorsareorthogonalwhentheyareindependentandthedesigniscompletelybalancedEachlevelofafactorappearsthesamenumberoftimesOrthogonaldesignsareimportantbecause EachterminthedesigncanbetestedindependentlyofallothertermsRemovingatermfromthemodeldoesnotaffecttheremainingtermsTheyguaranteethatthefactorsareindependentTheymaketheanalysismorerobusttounequalvariances TypesofOrthogonalDesigns Fullfactorialexperiments2 levelfullfactorialexperiments2 levelfractionalfactorialexperimentsPlackett BurmanandTaguchiarraysSomeresponsesurfaceexperiments UseoforthogonaldesignswhenwerundesignedexperimentsensuresthatthefactorsareindependentItalsomakestheanalysismorerobusttounequalvariances sincethedesignisbalanced MainEffectsandInteractions DesignforSixSigma DefinitionofEffects MainEffectAmaineffectforafactorisbasedonthedifferencesinsampleaveragesforalloftherunsateachlevelofthefactorEachfactorhasitsmaineffectscalculatedindependentlyofallotherfactorsMaineffectsforanyparticularfactordonotaccountforchangesinanyotherfactorInteractionEffectAninteractioneffectisbasedonthedifferencesinsampleaveragesforalloftherunsateachcombinationoflevelsfortwoormorefactorsAninteractioneffectalsocausesthemaineffectforonefactortobedifferentateachlevelofanotherfactor Createa2x2designforfactorsAandB CreatetheExperiment Createanon random2x2designforfactorsAandB CreatetheExperiment Continued CreatetheExperiment 5 Thedesign instandard non random order CreatetheExperiment Continued Thedesign instandard non random orderAddtheresponsedata stoppingdistance infeetmeasuredfrom60MPH StopDist129120144133124112139136 FittheModel AnalyzetheExperiment AnalyzetheExperiment FittheModel continued AnalyzetheExperiment GeneralLinearModel StopDistversusAirPressure WheelSizeFactorTypeLevelsValuesAirPresfixed22832WheelSifixed21516AnalysisofVarianceforStopDis usingAdjustedSSforTestsSourceDFSeqSSAdjSSAdjMSFPAirPres1561 13561 13561 1336 500 004WheelSi1153 12153 12153 129 960 034AirPres WheelSi16 126 126 120 400 562Error461 5061 5015 37Total7781 87 p value alphavalue theinteractionisnotsignificant Ordinarily wewouldremovethistermfromthemodel butwewillkeepitinfornow Wewilldiscussreducingthemodellater AnalyzetheExperiment Createthefactorialplots maineffectsandinteraction DrawConclusions ThisistheaverageresponsewhenAirPressure 28 ItistheoptimumconditionforAirPressure ThisistheaverageresponsewhenWheelSize 16 ItistheoptimumconditionforWheelSize Notice StoppingDistanceincreasesasAirPressureincreasesStoppingDistancedecreasesasWheelSizeincreases TheeffectofAirPressureislargerthantheeffectofWheelSize DrawConclusions ThisistheaverageresponsewhenAirPressure 32andWheelSize 15 Theinteractionisnotsignificant Noticehowthelinesarealmostparallel MaineffectofWheelSizewhenAirPressureisheldat32psi MaineffectofWheelSizewhenAirPressureisheldat28psi StepstoConductaFullFactorialExperiment DesignforSixSigma Step1 StatethepracticalproblemandobjectiveoftheexperimentStep2 StatethefactorsandlevelsofinterestStep3 Determinetheappropriatesamplesize givenaandbrisksStep4 CreatethedesigninMINITAB RandomizetheexperimentalrunsinthedatasheetStep5 ConducttheexperimentStep6 RuntheDOEanalysisforthefullmodelStep7 ReducethemodelReviewtheANOVAtableandeliminatetermswithp valuesabove 05 Eliminatehighestordertermsfirst thenlowerorder andfinallymaineffects Termsshouldberemovedoneatatime Youshouldnotremoveanytermthatisincludedinahigher orderterm thisiscalledpreservinghierarchicalintegrityRunthefinalreducedmodeltoincludeonlythosetermswhosep valuesaredeemedsignificantStep8 CheckforviolationsofassumptionsAnalyzetheresidualsofthereducedmodeltoensurewehaveanappropriatemodel StepstoConductaFullFactorialDOE Step9 DetermineoptimalsettingsbygraphicallyanalyzingremainingtermsInteractions usinginteractionplot Lookatthehighestorderinteractionsfirst For3 wayinteractionsunstackthedataandanalyze Oncethehighestorderinteractionsareinterpreted analyzethenextsetoflowerorderinteractions MainEffects usingmaineffectsplot MaineffectsplotsareusedtodeterminesettingsforfactorsnotalreadydeterminedfrominteractionplotsStep10 Calculatepercentageofvariationexplained epsilonsquare byeachtermStep11 ValidateresultsbyreplicatingoptimumconditionsStep12 Finalreport StepstoConductaFullFactorialExperiment FullFactorialExample Youareinchargeofaprojecttoexamineincomingcallsforacallcenter Oneoftheissuesistheamountoftimeonhold YouwouldobviouslyliketomakethisasshortaspossibleandasconsistentaspossibleYouwillconductanexperimenttodeterminewhetherthevendorsusedtohandleincomingcalls aswellasthetypeofphonesysteminvolvedhaveanyimpactontheholdtimeThereare3vendors HiTechOnTimeAcmeThereare3typesofphonesystems PBXContractPhoneCo FullFactorialExample Continued Step1 Statethepracticalproblemandobjectiveoftheexperiment Determinewhatinfluencesholdtime andfindthebestcombinationtoconsistentlyreduceholdtimeStep2 Statethefactorsandlevelsofinterest FactorsLevelsVendor HiTechOnTimeAcmePhoneSystem PBXContractPhoneCoStep3 Determinetheappropriatesamplesize givenaandbrisksIthasbeendeterminedthatwewillrun4replications FullFactorialExample Continued Step4 CreatethedesigninMINITAB Randomizetheexperimentalrunsinthedatasheet FullFactorialExample Continued Step4 CreatethedesigninMINITAB cont d FullFactorialExample Continued Step4 CreatethedesigninMINITAB cont d Note fordemonstrationpurposes wedidnotrandomizetheruns FullFactorialExample Continued Step5 ConducttheexperimentUse DFSSBB310aCallCenter MPJ CAUTION Beforeyouruntheexperimentandcollectdata besurethatyoucanmeasureboththefactorsandtheresponse MSA FullFactorialExample Continued Step6 RuntheDOEanalysisforthefullmodelStat DOE Factorial AnalyzeFactorialDesign FullFactorialExample Continued Step6 RuntheDOEanalysisforthefullmodel GeneralLinearModel HoldTimeversusVendor PhoneSystemFactorTypeLevelsValuesVendorfixed3HiTechOnTimeAcmePhoneSyfixed3PBXContractPhoneCoAnalysisofVarianceforHoldTim usingAdjustedSSforTestsSourceDFSeqSSAdjSSAdjMSFPVendor2639 06639 06319 537 490 003PhoneSy22029 062029 061014 5323 790 000Vendor PhoneSy4524 94524 94131 243 080 033Error271151 251151 2542 64Total354344 31UnusualObservationsforHoldTimObsHoldTimFitSEFitResidualStResid1971 000085 25003 2649 14 2500 2 52RRdenotesanobservationwithalargestandardizedresidual Minitabflagsanystandardizedresidualthatis 2 Theseareunusualobservations whichcanexertinfluenceonthemodelThinkoftheseasoutliersinaBoxPlot FullFactorialExample Continued Step7 Reducethemodel Wedonotneedtoreducethemodel alltermsaresignifi