DFSSBB314CentralCompositeDesign

314-1DesignforSixSigmaCentralCompositeDesignDFSSBB314CentralCompositeDesign.ppt314-2Copyright©2001-2004SixSigmaAcademyInternationalLLCAllRightsReservedPurposeUnderstandthedifferencebetweendesignsthatareusedtoselectKPIVsanddesignsthatareusedtooptimizethesettingsofalreadyconfirmedKPIVsDesignandanalyzeaCentralCompositeDesign(CCD)ApplyCCDtoanexercise314-3Copyright©2001-2004SixSigmaAcademyInternationalLLCAllRightsReservedDetermineCustomers&Y’s:Quality,Price&ProductDemandInitialProductPlatformkeyX’s,productvelocitiesMeasuretheX’sandY’sFindcriticalY=f(x)relationshipsOptimizeY’s&criticalX’s,RMI,WIP,FGI&SupplyChainSetcriticalX’s,kan-bansCheckKeyY’sFailuremodesandanalysesDFSSRoadmapIdentifyCTQCMetrics/MeasuresEstablishBusinessNeeds&PriorityDevelopProjectCharter&PlanDEFINERallyPoints0-1CONCEPTRallyPoints1-2DESIGNRallyPoints3-4OPTIMIZERallyPoints4-6VERIFYRallyPoints5-8IdentifyKeyMeasurementSystemsIdentifyTargetMarkets&SegmentsIdentifyCustomerNeeds/WantsEstablishCriticaltoQualityCharacteristics(CTQC’s)EstablishTechnicalFeaturesDevelopOptimalDesignConceptDevelopBusinessCase&ScheduleDesignSystem,Subsystems&ComponentsDesignProcessesModel&AssessCriticalParametersModel&AnalyzeTolerances&SensitivitiesDevelop/EvaluateMeasurementSystemsInitialRobustProductDesignMinimizeProductComplexityMaximizeProductVelocityOptimizeCriticalInputs-FinalRobustDesignOptimize,SimulateProcessesFinalRobustProductDesignSetInitialControlSystems/PlansVerifyProductPerformanceVerifyProcessPerformanceTestPlans&ReportsAnalyze/MinimizeProduct&ProcessRisks314-4Copyright©2001-2004SixSigmaAcademyInternationalLLCAllRightsReservedWhyCentralCompositeDesign?DevelopsQuadraticModelsRelativelyinexpensiveSupportssequentialexperimentationstrategyOptimizesprocessknowledgeCommonlyusedwithResponseSurfaceMethods314-5Copyright©2001-2004SixSigmaAcademyInternationalLLCAllRightsReservedWhatisCentralCompositeDesign(CCD)?AdvancedregressionapplicationActiveanalysisUsedtoextendexistingdata-Quadraticterms-UsescontinuousdataUsedwithResponseSurfaceMethodsKeepsmall(2-6factors),getslargefast314-6Copyright©2001-2004SixSigmaAcademyInternationalLLCAllRightsReservedImportantFormulas(Review)First-OrderLinearModelY=B0+SBiXi+eY=B0+B1X1+B2X2+…+BkXk+eLinearModelWith2-WayInteractionsY=B0+SBiXi+SSBijXiXj+eY=B0+B1X1+B2X2+…+BkXk+B12X1X2+…+eSecond-OrderQuadraticModelY=B0+SBiXi+SBiiXi2+SSBijXiXj+eY=B0+B1X1+B2X2+…+BkXk+B12X1X2+…+B11X12+B22X22+…+BkkXk2+e2-Levelfactorialdesignscanbeusedforthefirsttwomodels,CentralCompositedesignsareneededforthethirdmodel314-7Copyright©2001-2004SixSigmaAcademyInternationalLLCAllRightsReservedWhatisaCentralCompositeDesign?Two-LevelFactorialEachfactorrunattwosettings(LoandHi)–TwopointsdefinetheequationforastraightlineCenterpointsareonlyusedtotestforcurvatureCentralCompositeIftheaxialpointsareoutsidethesquare,ashere,eachfactorhas5settingsIftheaxialpointsareonthesidesofthesquare,eachfactorhas3settingsEitherway,3ormorepointscanbeusedtodefineaquadraticequation,i.e.–curvedlineCubePointsCenterPointsAxialpoints314-8Copyright©2001-2004SixSigmaAcademyInternationalLLCAllRightsReservedPropertiesofCCDesignsAlphaAlpha=distance(incodedunits)fromcenterofdesigntoaxialpointsAlpha1,axialptsoutsidecornerptsDefaultalphasettoensureRotatability(predictionerrorisequalinalldirections)ORtoensurethatblocksareorthogonal(blockcoefficient(s)havenoimpactonothercoefficientsinthemodel)Alpha=1,axialptsonthefacesFacecentereddesignUseonlywhenitistoodangeroustogooutsidethecornerpoints-1+10314-9Copyright©2001-2004SixSigmaAcademyInternationalLLCAllRightsReservedPossibleCentralComposite(CC)DesignsThesearetheCCdesignsavailableinMINITAB–from2to6factors.Notehowthenumberofrunscangetlarge–itisalwaysgoodtoreducethenumberoffactorsasmuchaspossible.314-10Copyright©2001-2004SixSigmaAcademyInternationalLLCAllRightsReservedPropertiesofDefaultMINITABCCDesignsNotes:2factors=4cubepts(Full)3factors=8cubepts(Full)4factors=16cubepts(Full)5factors=16cubepts(ResV,half-fraction)or32cubepts(Full)6factors=32cubepts(ResV,half-fraction)or64cubepts(Full)MostdesignsrotatableOrthogonalblocks314-11Copyright©2001-2004SixSigmaAcademyInternationalLLCAllRightsReservedStepstoConductaCCDExperiment(1)Step1:StatethepracticalproblemandobjectiveoftheexperimentStep2:StatethefactorsandlevelsofinterestStep3:Screeninitialfactors–reducetoasfewaspossibleStep4:EstablishdesignstrategyStep5:CreateCCdesigninMINITAB;randomizetherunsStep6:ConducttheexperimentStep7:FitthefullquadraticmodelStep8:ReducethemodelReviewtheANOVAtableandeliminatetermswithp-valuesabove.05.Eliminatenon-significantblocksfirst,thenhighestorderinteractionsterms,thenlowerorder,nextremoveinsignificantquadraticeffects,andfinallymaineffectsTermsshouldberemovedoneatatime.Youshouldnotremoveanytermthatisincludedinahigher-orderterm–thisiscalledpreservinghierarchicalintegrityRunthefinalreducedmodeltoincludeonlythosetermswhosep-valuesaredeemedsignificant314-12Copyright©2001-2004SixSigmaAcademyInternationalLLCAllRightsReservedStepstoConductaCCDExperiment(2)Step9:Checkmodelassumptions•Analyzether