QSM754SIXSIGMAAPPLICATIONSAGENDA.ppt

,QSM754SIXSIGMAAPPLICATIONSAGENDA,精品资料网,Day1Agenda,WelcomeandIntroductionsCourseStructureMeetingGuidelines/CourseAgenda/ReportOutCriteriaGroupExpectationsIntroductiontoSixSigmaApplicationsRedBeadExperimentIntroductiontoProbabilityDistributionsCommonProbabilityDistributionsandTheirUsesCorrelationAnalysis,精品资料网,Day2Agenda,TeamReportOutsonDay1MaterialCentralLimitTheoremProcessCapabilityMulti-VariAnalysisSampleSizeConsiderations,精品资料网,Day3Agenda,TeamReportOutsonDay2MaterialConfidenceIntervalsControlChartsHypothesisTestingANOVA(AnalysisofVariation)ContingencyTables,精品资料网,Day4Agenda,TeamReportOutsonPracticumApplicationDesignofExperimentsWrapUp-PositivesandDeltas,精品资料网,ClassGuidelines,Qthemean,themedianandthemode.,精品资料网,WHATISTHEMEAN?,精品资料网,WHATISTHEMEDIAN?,精品资料网,WHATISTHEMODE?,精品资料网,MEASURESOFCENTRALTENDENCY,SUMMARY,精品资料网,SOWHATSTHEREALDIFFERENCE?,精品资料网,SOWHATSTHEBOTTOMLINE?,精品资料网,COINTOSSPOPULATIONDISPERSION,精品资料网,WHATISTHERANGE?,精品资料网,WHATISTHEVARIANCE/STANDARDDEVIATION?,精品资料网,MEASURESOFDISPERSION,精品资料网,SAMPLEMEANANDVARIANCEEXAMPLE,精品资料网,SOWHATSTHEREALDIFFERENCE?,精品资料网,SOWHATSTHEBOTTOMLINE?,精品资料网,SOWHATISTHISSHIFTDF=(r-1)x(c-1).Inourcase,wehave3columns(c)and2rows(r)soourDF=(2-1)x(3-1)=1x2=2.Thesecondpieceofdataistherisk.Sincewearelookingfor.95(95%)confidence(andarisk=1-confidence)weknowtheariskwillbe.05.Inthec2table,wefindthatthecriticalvaluefora=.05and2DFtobe5.99.Therefore,ourc2CRIT=5.99Ourcalculatedc2valueisthesumoftheindividualcellc2values.Forourexamplethisis.04+.18+.27+.25+.81+1.20=2.75.Therefore,ourc2CALC=2.75.Wenowhaveallthepiecestoperformourtest.OurHo:isc2CALCc2CRIT.Isthistrue?Ourdatashows2.755.99,thereforewefailtorejectthenullhypothesisthatthereisnosignificantdifferencebetweenthevendorperformanceinthisarea.,精品资料网,ContingencyTableExercise,Wehaveapartwhichisexperiencinghighscrap.Yourteamthinksthatsinceitismanufacturedover3shiftsandon3differentmachines,thatthescrapcouldbecaused(Y=f(x)byanoffshiftworkmanshipissueormachinecapability.Verifywith95%confidencewhethereitherofthesehypothesisissupportedbythedata.,Constructacontingencytableofthedataandinterprettheresultsforeachdataset.,精品资料网,LearningObjectives,Understandhowtouseacontingencytabletosupportanimprovementproject.Understandtheenablingconditionsthatdeterminewhentouseacontingencytable.Understandhowtoconstructacontingencytable.Understandhowtointerpretacontingencytable.,精品资料网,DESIGNOFEXPERIMENTS(DOE)FUNDAMENTALS,精品资料网,LearningObjectives,Haveabroadunderstandingoftherolethatdesignofexperiments(DOE)playsinthesuccessfulcompletionofanimprovementproject.Understandhowtoconstructadesignofexperiments.Understandhowtoanalyzeadesignofexperiments.Understandhowtointerprettheresultsofadesignofexperiments.,精品资料网,WhydoweCare?,DesignofExperimentsisparticularlyusefulto:evaluateinteractionsbetween2ormoreKPIVsandtheirimpactononeormoreKPOVs.optimizevaluesforKPIVstodeterminetheoptimumoutputfromaprocess.,精品资料网,IMPROVEMENTROADMAPUsesofDesignofExperiments,精品资料网,KEYSTOSUCCESS,精品资料网,SoWhatIsaDesignofExperiment?,whereamathematicalreasoningcanbehad,itsasgreatafollytomakeuseofanyother,astogropeforathinginthedark,whenyouhaveacandlestandingbyyou.Arbuthnot,AdesignofexperimentintroducespurposefulchangesinKPIVs,sothatwecanmethodicallyobservethecorrespondingresponseintheassociatedKPOVs.,精品资料网,DesignofExperiments,FullFactorial,VariablesInput,Controllable(KPIV)Input,Uncontrollable(Noise)Output,Controllable(KPOV),HowdoyouknowhowmuchasuspectedKPIVactuallyinfluencesaKPOV?Youtestit!,精品资料网,DesignofExperiments,Terminology,Mathematicalobjectsaresometimesaspeculiarasthemostexoticbeastorbird,andthetimespentinexaminingthemmaybewellemployed.H.Steinhaus,MainEffects-Factors(KPIV)whichdirectlyimpactoutputInteractions-Multiplefactorswhichtogetherhavemoreimpactonprocessoutputthananyfactorindividually.Factors-IndividualKeyProcessInputVariables(KPIV)Levels-MultipleconditionswhichafactorissetatforexperimentalpurposesAliasing-Degreetowhichanoutputcannotbeclearlyassociatedwithaninputconditionduetotestdesign.Resolution-Degreeofaliasinginanexperimentaldesign,精品资料网,DOEChoices,Aconfusingarray.,FullFactorialTaguchiL16HalfFraction2leveldesigns3leveldesignsscreeningdesignsResponsesurfacedesignsetc.,Forthepurposesofthistrainingwewillteachonlyfullfactorial(2k)designs.Thiswillenableyoutogetabasicunderstandingofapplicationandusethetool.Inaddition,thevastmajorityofproblemscommonlyencounteredinimprovementprojectscanbeaddressedwiththisdesign.Ifyouhaveanyquestiononwhetherthedesignisadequate,consultastatisticalexpert.,Mumble,Mumble,blackbelt,Mumble,statisticsstuff.,精品资料网,TheYatesAlgorithmDeterminingthenumberofTreatments,Oneaspectwhichiscriticaltothedesignisthattheybe“balanced”.AbalanceddesignhasanequalnumberoflevelsrepresentedforeachKPIV.Wecanconfirmthisinthedesignontherightbyaddingupthenumberof+and-marksineachcolumn.Weseethatineachcase,theyequal4+and4-values,thereforethedesignisbalanced.,Yatesalgorithmisaquickandeasyway(honest,trustme)toensurethatwegetabalanceddesignwheneverwearebuildingafullfactorialDOE.Noticethatthenumberoftreatments(uniquetestmixesofKPIVs)isequalto23or8.Noticethatinthe“Afactor”column,wehave4+inarowandthen4-inarow.Thisisequaltoagroupof22or4.Alsonoticethatthegroupinginthenextcolumnis21or2+valuesand2-valuesrepeateduntilall8treatmentsareaccountedfor.Repeatthispatternfortheremainingfactors.,精品资料网,TheYatesAlgorithmSettinguptheAlgorithmforInteractions,Nowwecanaddthecolumnsthatreflecttheinteractions.RememberthattheinteractionsarethemainreasonweuseaDOEoverasimplehypothesistest.TheDOEisthebesttooltostudy“mix”typesofproblems.,Youcanseefromtheexampleabovewehaveaddedadditionalcolumnsforeachofthewaysthatwecan“mix”the3factorswhichareunderstudy.Theseareourinteractions.Thesignthatgoesintothevarioustreatmentboxesfortheseinteractionsisthealgebraicproductofthemaineffectstreatments.Forexample,treatment7forinteractionABis(-x-=+),soweputaplusinthebox.So,inthesecalculations,thefollowingapply:minus(-)timesminus(-)=plus(+)plus(+)timesplus(+)=plus(+)minus(-)timesplus(+)=minus(-)plus(+)timesminus(-)=minus(-),精品资料网,YatesAlgorithmExercise,Weworkforamajor“Donut&Coffee”chain.Wehavebeentaskedtodeterminewhatarethemostsignificantfactorsinmaking“themostdeliciouscoffeeintheworld”.Inourworkwehaveidentifiedthreefactorsweconsidertobesignificant.Thesefactorsarecoffeebrand(maxwellhousevschockfullonuts),water(springvstap)andcoffeeamount(#ofscoops).,UsetheYatesalgorithmtodesigntheexperiment.,精品资料网,Selectthefactors(KPIVs)tobeinvestigatedanddefinetheoutputtobemeasured(KPOV).Determinethe2levelsforeachfactor.Ensurethatthelevelsareaswidelyspreadapartastheprocessandcircumstanceallow.DrawupthedesignusingtheYatesalgorithm.,So,HowdoIConductaDOE?,精品资料网,Determinehowmanyreplicationsorrepetitionsyouwanttodo.Areplicationisacompletenewrunofatreatmentandarepetitionismorethanonesamplerunaspartofasingletreatmentrun.Randomizetheorderofthetreatmentsandruneach.Placethedataforeachtreatmentinacolumntotherightofyourmatrix.,So,HowdoIConductaDOE?,精品资料网,Calculatetheaverageoutputforeachtreatment.Placetheaverageforeachtreatmentafterthesign(+or-)ineachcell.,AnalysisofaDOE,精品资料网,Addupthevaluesineachcolumnandputtheresultundertheappropriatecolumn.Thisisthetotalestimatedeffectofthefactororcombinationoffactors.Dividethetotalestimatedeffectofeachcolumnby1/2thetotalnumberoftreatments.Thisistheaverageestimatedeffect.,AnalysisofaDOE,精品资料网,Theseaveragesrepresenttheaveragedifferencebetweenthefactorlevelsrepresentedbythecolumn.So,inthecaseoffactor“A”,theaveragedifferenceintheresultoutputbetweenthe+levelandthe-levelis6.75.Wecannowdeterminethefactors(orcombinationoffactors)whichhavethegreatestimpactontheoutputbylookingforthemagnitudeoftherespectiveaverages(i.e.,ignorethesign).,AnalysisofaDOE,Thismeansthattheimpactisinthefollowingorder:A(6.75)AB(5.25)BC(3.25)B(2.25)AC(1.75)ABC(1.25)C(-0.25),精品资料网,AnalysisofaDOE,精品资料网,ConfidenceIntervalforDOEresults,精品资料网,ConfidenceIntervalforDOEresults,精品资料网,IMPROVEMENTPHASEVitalFewVariablesEstablishOperatingTolerances,HowaboutanotherwayoflookingataDOE?,精品资料网,Itlookslikethelanesareingoodconditiontoday,Mark.TimhasbroughtthreedifferentbowlingballswithhimbutIdontthinkhewillneedthemalltoday.Youknowheseemstohaveimprovedhisgameeversincehestartedbowlingwiththatwristband.,HowdoIknowwhatworksforme.Laneconditions?Balltype?Wristband?,精品资料网,HowdoIsetuptheExperiment?,FactorAFactorBFactorC