3 - QSM 754 COURSE POWERPOINT SLIDES V8.ppt

QSM754SIXSIGMAAPPLICATIONSAGENDA Day1Agenda WelcomeandIntroductionsCourseStructureMeetingGuidelines CourseAgenda ReportOutCriteriaGroupExpectationsIntroductiontoSixSigmaApplicationsRedBeadExperimentIntroductiontoProbabilityDistributionsCommonProbabilityDistributionsandTheirUsesCorrelationAnalysis Day2Agenda TeamReportOutsonDay1MaterialCentralLimitTheoremProcessCapabilityMulti VariAnalysisSampleSizeConsiderations Day3Agenda TeamReportOutsonDay2MaterialConfidenceIntervalsControlChartsHypothesisTestingANOVA AnalysisofVariation ContingencyTables Day4Agenda TeamReportOutsonPracticumApplicationDesignofExperimentsWrapUp PositivesandDeltas ClassGuidelines Q AaswegoBreaksHourlyHomeworkReadingsAsassignedinSyllabusGradingClassPreparation30 TeamClassroomExercises30 TeamPresentations40 10MinuteDailyPresentation Day2and3 onApplicationofpreviousdayswork20minutefinalPracticumapplication Lastday CopyonFloppyaswellashardcopyPowerpointpreferredRotatePresentersQ Afromtheclass INTRODUCTIONTOSIXSIGMAAPPLICATIONS LearningObjectives Haveabroadunderstandingofstatisticalconceptsandtools Understandhowstatisticalconceptscanbeusedtoimprovebusinessprocesses Understandtherelationshipbetweenthecurriculumandthefourstepsixsigmaproblemsolvingprocess Measure Analyze ImproveandControl WhatisSixSigma APhilosophy AQualityLevel AStructuredProblem SolvingApproach AProgram POSITIONINGSIXSIGMATHEFRUITOFSIXSIGMA UNLOCKINGTHEHIDDENFACTORY CommonSixSigmaProjectAreas ManufacturingDefectReductionCycleTimeReductionCostReductionInventoryReductionProductDevelopmentandIntroductionLaborReductionIncreasedUtilizationofResourcesProductSalesImprovementCapacityImprovementsDeliveryImprovements TheFocusofSixSigma INSPECTIONEXERCISE Thenecessityoftrainingfarmhandsforfirstclassfarmsinthefatherlyhandlingoffarmlivestockisforemostinthemindsoffarmowners Sincetheforefathersofthefarmownerstrainedthefarmhandsforfirstclassfarmsinthefatherlyhandlingoffarmlivestock thefarmownersfeeltheyshouldcarryonwiththefamilytraditionoftrainingfarmhandsoffirstclassfarmsinthefatherlyhandlingoffarmlivestockbecausetheybelieveitisthebasisofgoodfundamentalfarmmanagement Howmanyf scanyouidentifyin1minuteofinspection INSPECTIONEXERCISE Thenecessityof trainingf armhandsf orf irstclassf armsinthef atherlyhandlingof f armlivestockisf oremostinthemindsof f armowners Sincethef oref athersof thef armownerstrainedthef armhandsf orf irstclassf armsinthef atherlyhandlingof f armlivestock thef armownersf eeltheyshouldcarryonwiththef amilytraditionof trainingf armhandsof f irstclassf armsinthef atherlyhandlingof f armlivestockbecausetheybelieveitisthebasisof goodf undamentalf armmanagement Howmanyf scanyouidentifyin1minuteofinspection 36totalareavailable SIXSIGMACOMPARISON IMPROVEMENTROADMAP Measurementsarecritical Ifwecan taccuratelymeasuresomething wereallydon tknowmuchaboutit Ifwedon tknowmuchaboutit wecan tcontrolit Ifwecan tcontrolit weareatthemercyofchance WHYSTATISTICS THEROLEOFSTATISTICSINSIXSIGMA WEDON TKNOWWHATWEDON TKNOWIFWEDON THAVEDATA WEDON TKNOWIFWEDON TKNOW WECANNOTACTIFWECANNOTACT THERISKISHIGHIFWEDOKNOWANDACT THERISKISMANAGEDIFWEDOKNOWANDDONOTACT WEDESERVETHELOSS DR MikelJ HarryTOGETDATAWEMUSTMEASUREDATAMUSTBECONVERTEDTOINFORMATIONINFORMATIONISDERIVEDFROMDATATHROUGHSTATISTICS WHYSTATISTICS THEROLEOFSTATISTICSINSIXSIGMA Ignoranceisnotbliss itisthefoodoffailureandthebreedinggroundforloss DR MikelJ Harry Yearsagoastatisticianmighthaveclaimedthatstatisticsdealtwiththeprocessingofdata Today sstatisticianwillbemorelikelytosaythatstatisticsisconcernedwithdecisionmakinginthefaceofuncertainty Bartlett SalesReceiptsOnTimeDeliveryProcessCapacityOrderFulfillmentTimeReductionofWasteProductDevelopmentTimeProcessYieldsScrapReductionInventoryReductionFloorSpaceUtilization WHATDOESITMEAN RandomChanceorCertainty Whichwouldyouchoose LearningObjectives Haveabroadunderstandingofstatisticalconceptsandtools Understandhowstatisticalconceptscanbeusedtoimprovebusinessprocesses Understandtherelationshipbetweenthecurriculumandthefourstepsixsigmaproblemsolvingprocess Measure Analyze ImproveandControl REDBEADEXPERIMENT LearningObjectives Haveanunderstandingofthedifferencebetweenrandomvariationandastatisticallysignificantevent Understandthedifferencebetweenattemptingtomanageanoutcome Y asopposedtomanagingupstreameffects x s Understandhowtheconceptofstatisticalsignificancecanbeusedtoimprovebusinessprocesses WELCOMETOTHEWHITEBEADFACTORY HIRINGNEEDSBEADSAREOURBUSINESSPRODUCTIONSUPERVISOR4PRODUCTIONWORKERS2INSPECTORS1INSPECTIONSUPERVISOR1TALLYKEEPER STANDINGORDERS Followtheprocessexactly Donotimproviseorvaryfromthedocumentedprocess Yourperformancewillbebasedsolelyonyourabilitytoproducewhitebeads Noquestionswillbeallowedaftertheinitialtrainingperiod Yourdefectquotaisnomorethan5offcolorbeadsallowedperpaddle WHITEBEADMANUFACTURINGPROCESSPROCEDURES Theoperatorwilltakethebeadpaddleintherighthand Insertthebeadpaddleata45degreeangleintothebeadbowl Agitatethebeadpaddlegentlyinthebeadbowluntilallspacesarefilled Gentlywithdrawthebeadpaddlefromthebowlata45degreeangleandallowthefreebeadstorunoff Withouttouchingthebeads showthepaddletoinspector 1andwaituntiltheoffcolorbeadsaretallied Movetoinspector 2andwaituntiltheoffcolorbeadsaretallied Inspector 1and 2showtheirtalliestotheinspectionsupervisor Iftheyagree theinspectionsupervisorannouncesthecountandthetallykeeperwillrecordtheresult Iftheydonotagree theinspectionsupervisorwilldirecttheinspectorstorecountthepaddle Whenthecountiscomplete theoperatorwillreturnallthebeadstothebowlandhandthepaddletothenextoperator INCENTIVEPROGRAM Lowbeadcountswillberewardedwithabonus Highbeadcountswillbepunishedwithareprimand Yourperformancewillbebasedsolelyonyourabilitytoproducewhitebeads Yourdefectquotaisnomorethan7offcolorbeadsallowedperpaddle PLANTRESTRUCTURE Defectcountsremaintoohighfortheplanttobeprofitable Thetwobestperformingproductionworkerswillberetainedandthetwoworstperformingproductionworkerswillbelaidoff Yourperformancewillbebasedsolelyonyourabilitytoproducewhitebeads Yourdefectquotaisnomorethan10offcolorbeadsallowedperpaddle OBSERVATIONS WHATOBSERVATIONSDIDYOUMAKEABOUTTHISPROCESS TheFocusofSixSigma Y f x Allcriticalcharacteristics Y aredrivenbyfactors x whichare downstream fromtheresults Attemptingtomanageresults Y onlycausesincreasedcostsduetorework testandinspection Understandingandcontrollingthecausativefactors x istherealkeytohighqualityatlowcost LearningObjectives Haveanunderstandingofthedifferencebetweenrandomvariationandastatisticallysignificantevent Understandthedifferencebetweenattemptingtomanageanoutcome Y asopposedtomanagingupstreameffects x s Understandhowtheconceptofstatisticalsignificancecanbeusedtoimprovebusinessprocesses INTRODUCTIONTOPROBABILITYDISTRIBUTIONS LearningObjectives Haveabroadunderstandingofwhatprobabilitydistributionsareandwhytheyareimportant Understandtherolethatprobabilitydistributionsplayindeterminingwhetheraneventisarandomoccurrenceorsignificantlydifferent Understandthecommonmeasuresusedtocharacterizeapopulationcentraltendencyanddispersion UnderstandtheconceptofShift Drift Understandtheconceptofsignificancetesting WhydoweCare AnunderstandingofProbabilityDistributionsisnecessaryto Understandtheconceptanduseofstatisticaltools Understandthesignificanceofrandomvariationineverydaymeasures Understandtheimpactofsignificanceonthesuccessfulresolutionofaproject IMPROVEMENTROADMAPUsesofProbabilityDistributions Establishbaselinedatacharacteristics ProjectUses Identifyandisolatesourcesofvariation Usetheconceptofshift drifttoestablishprojectexpectations Demonstratebeforeandafterresultsarenotrandomchance KEYSTOSUCCESS Measurementsarecritical Ifwecan taccuratelymeasuresomething wereallydon tknowmuchaboutit Ifwedon tknowmuchaboutit wecan tcontrolit Ifwecan tcontrolit weareatthemercyofchance TypesofMeasures Measureswherethemetriciscomposedofaclassificationinoneoftwo ormore categoriesiscalledAttributedata Thisdataisusuallypresentedasa count or percent Good BadYes NoHit Missetc MeasureswherethemetricconsistsofanumberwhichindicatesaprecisevalueiscalledVariabledata TimeMiles Hr COINTOSSEXAMPLE Takeacoinfromyourpocketandtossit200times Keeptrackofthenumberoftimesthecoinfallsas heads Whencomplete theinstructorwillaskyouforyour head count COINTOSSEXAMPLE COINTOSSPROBABILITYEXAMPLE COINTOSSEXAMPLE Wecannowequateaprobabilitytotheoccurrenceofspecificvaluesorgroupsofvalues Forexample wecanseethattheoccurrenceofa Headcount oflessthan74orgreaterthan124outof200tossesissorarethatasingleoccurrencewasnotregisteredoutof10 000tries Ontheotherhand wecanseethatthechanceofgettingacountnear orat 100ismuchhigher Withthedatathatwenowhave wecanactuallypredicteachofthesevalues COINTOSSPROBABILITYDISTRIBUTION CommonOccurrenceRareEvent WHATDOESITMEAN Whatarethechancesthatthis justhappened Iftheyaresmall chancesarethatanexternalinfluenceisatworkthatcanbeusedtoourbenefit ProbabilityandStatistics theoddsofColoradoUniversitywinningthenationaltitleare3to1 DrewBledsoe spasscompletionpercentageforthelast6gamesis 58 versus 78 forthefirst5games TheSenatorwillwintheelectionwith54 ofthepopularvotewithamarginof 3 ProbabilityandStatisticsinfluenceourlivesdailyStatisticsistheuniversallanuageforscienceStatisticsistheartofcollecting classifying presenting interpretingandanalyzingnumericaldata aswellasmakingconclusionsaboutthesystemfromwhichthedatawasobtained PopulationVs Sample CertaintyVs Uncertainty DescriptiveStatistics DescriptiveStatisticsisthebranchofstatisticswhichmostpeoplearefamiliar Itcharacterizesandsummarizesthemostprominentfeaturesofagivensetofdata means medians standarddeviations percentiles graphs tablesandcharts DescriptiveStatisticsdescribetheelementsofapopulationasawholeortodescribedatathatrepresentjustasampleofelementsfromtheentirepopulation InferentialStatistics InferentialStatisticsisthebranchofstatisticsthatdealswithdrawingconclusionsaboutapopulationbasedoninformationobtainedfromasampledrawnfromthatpopulation Whiledescriptivestatisticshasbeentaughtforcenturies inferentialstatisticsisarelativelynewphenomenonhavingitsrootsinthe20thcentury We infer somethingaboutapopulationwhenonlyinformationfromasampleisknown ProbabilityisthelinkbetweenDescriptiveandInferentialStatistics WHATDOESITMEAN NUMBEROFHEADS SIGMAVALUE Z CUM OFPOPULATION Andthefirst50trialsshowed HeadCounts greaterthan130 WHATIFWEMADEACHANGETOTHEPROCESS Chancesareverygoodthattheprocessdistributionhaschanged Infact thereisaprobabilitygreaterthan99 999 thatithaschanged USESOFPROBABILITYDISTRIBUTIONS Primarilythesedistributionsareusedtotestforsignificantdifferencesindatasets Tobeclassifiedassignificant theactualmeasuredvaluemustexceedacriticalvalue Thecriticalvalueistabularvaluedeterminedbytheprobabilitydistributionandtheriskoferror Thisriskoferroriscalledariskandindicatestheprobabilityofthisvalueoccurringnaturally So anariskof 05 5 meansthatthiscriticalvaluewillbeexceededbyarandomoccurrencelessthan5 ofthetime SOWHATMAKESADISTRIBUTIONUNIQUE CENTRALTENDENCYWhereapopulationislocated DISPERSIONHowwideapopulationisspread DISTRIBUTIONFUNCTIONThemathematicalformulathatbestdescribesthedata wewillcoverthisindetailinthenextmodule COINTOSSCENTRALTENDENCY Whataresomeofthewaysthatwecaneasilyindicatethecenteringcharacteristicofthepopulation Threemeasureshavehistoricallybeenused themean themedianandthemode WHATISTHEMEAN WHATISTHEMEDIAN WHATISTHEMODE MEASURESOFCENTRALTENDENCY SUMMARY SOWHAT STHEREALDIFFERENCE SOWHAT STHEBOTTOMLINE COINTOSSPOPULATIONDISPERSION WHATISTHERANGE WHATISTHEVARIANCE STANDARDDEVIATION MEASURESOFDISPERSION SAMPLEMEANANDVARIANCEEXAMPLE SOWHAT STHEREALDIFFERENCE SOWHAT STHEBOTTOMLINE SOWHATISTHISSHIFT DRIFTSTUFF SOWHATHAPPENED VARIATIONFAMILIES SOWHATDOESITMEAN Tocompensatefortheselongtermvariations wemustconsidertwosetsofmetrics Shorttermmetricsarethosewhichtypicallyareassociatedwithourwork Longtermmetricstaketheshorttermmetricdataanddegradeitbyanaverageof1 5s IMPACTOF1 5sSHIFTANDDRIFT SHIFTANDDRIFTEXERCISE Wehavejustcompletedaprojectandhavepresentedthefollowingshorttermmetrics Zst 3 5PPMst 233Cpkst 1 2 Calculatethelongtermvaluesforeachofthesemetrics LearningObjectives Haveabroadunderstandingofwhatprobabilitydistributionsareandwhytheyareimportant Understandtherolethatprobabilitydistributionsplayindeterminingwhetheraneventisarandomoccurrenceorsignificantlydifferent Understandthecommonmeasuresusedtocharacterizeapopulationcentraltendencyanddispersion UnderstandtheconceptofShift Drift Understandtheconceptofsignificancetesting COMMONPROBABILITYDISTRIBUTIONSANDTHEIRUSES LearningObjectives Haveabroadunderstandingofhowprobabilitydistributionsareusedinimprovementprojects Reviewtheoriginanduseofcommonprobabilitydistributions WhydoweCare Probabilitydistributionsarenecessaryto determinewhetheraneventissignificantorduetorandomchance predicttheprobabilityofspecificperformancegivenhistoricalcharacteristics IMPROVEMENTROADMAPUsesofProbabilityDistributions KEYSTOSUCCESS PROBABILITYDISTRIBUTIONS WHEREDOTHEYCOMEFROM COMMONPROBABILITYDISTRIBUTIONS THELANGUAGEOFMATH PopulationandSampleSymbology THREEPROBABILITYDISTRIBUTIONS ZTRANSFORM TheFocusofSixSigma Y f x Allcriticalcharacteristics Y aredrivenbyfactors x whichare downstream fromtheresults Attemptingtomanageresults Y onlycausesincreasedcostsduetorework testandinspection Understandingandcontrollingthecausativefactors x istherealkeytohighqualityatlowcost Probabilitydistributionsidentifysourcesofcausativefactors x Thesecanbeidentifiedandverifiedbytestingwhichshowstheirsignificanteffectsagainstthebackdropofrandomnoise BUTWHATDISTRIBUTIONSHOULDIUSE HOWDOPOPULATIONSINTERACT Theseinteractionsformanewpopulationwhichcannowbeusedtopredictfutureperformance HOWDOPOPULATIONSINTERACT ADDINGTWOPOPULATIONS HOWDOPOPULATIONSINTERACT SUBTRACTINGTWOPOPULATIONS TRANSACTIONALEXAMPLE Ordersarecominginwiththefollowingcharacteristics Shipmentsaregoingoutwiththefollowingcharacteristics Assumingnothingchanges whatpercentofthetimewillshipmentsexceedorders TRANSACTIONALEXAMPLE TRANSACTIONALEXAMPLE CONTINUED MANUFACTURINGEXAMPLE 2Blocksarebeingassembledendtoendandsignificantvariationhasbeenfoundintheoverallassemblylength Theblockshavethefollowingdimensions Determinetheoverallassemblylengthandstandarddeviation LearningObjectives Haveabroadunderstandingofhowprobabilitydistributionsareusedinimprovementprojects Reviewtheoriginanduseofcommonprobabilitydistributions CORRELATIONANALYSIS LearningObjectives Understandhowcorrelationcanbeusedtodemonstratearelationshipbetweentwofactors Knowhowtoperformacorrelationanalysisandcalculatethecoefficientoflinearcorrelation r Understandhowacorrelationanalysiscanbeusedinanimprovementproject WhydoweCare CorrelationAnalysisisnecessaryto showarelationshipbetweentwovariables Thisalsosetsthestageforpotentialcauseandeffect IMPROVEMENTROADMAPUsesofCorrelationAnalysis Determineandquantifytherelationshipbetweenfactors x andoutputcharacteristics Y CommonUses KEYSTOSUCCESS WHATISCORRELATION Ameasurablerelationshipbetweentwovariabledatacharacteristics NotnecessarilyCause Effect Y f x Correlationrequirespaireddatasets ie Y1 x1 Y2 x2 etc Theinputvariableiscalledtheindependentvariable xorKPIV sinceitisindependentofanyotherconstraintsTheoutputvariableiscalledthedependentvariable YorKPOV sinceitis theoretically dependentonthevalueofx Thecoefficientoflinearcorrelation r isthemeasureofthestrengthoftherelationship Thesquareof r isthepercentoftheresponse Y whichisrelatedtotheinput x WHATISCORRELATION TYPESOFCORRELATION CALCULATING r CoefficientofLinearCorrelation APPROXIMATING r CoefficientofLinearCorrelation HOWDOIKNOWWHENIHAVECORRELATION Theanswershouldstrikeafamiliarcordatthispoint Wehaveconfidence 95 thatwehavecorrelationwhen rCALC rCRIT SincesamplesizeisakeydeterminateofrCRITweneedtouseatabletodeterminethecorrectrCRITgiventhenumberoforderedpairswhichcomprisethecompletedataset So intheprecedingexamplewehad60orderedpairsofdataandwecomputedarCALCof 47 UsingthetableattheleftwedeterminethattherCRITvaluefor60is 26 Comparing rCALC rCRITweget 47 26 Thereforethecalculatedvalueexceedstheminimumcriticalvaluerequiredforsignificance Conclusion Weare95 confidentthattheobservedcorrelationissignificant LearningObjectives Understandhowcorrelationcanbeusedtodemonstratearelationshipbetweentwofactors Knowhowtoperformacorrelationanalysisandcalculatethecoefficientoflinearcorrelation r Understandhowacorrelationanalysiscanbeusedinablackbeltstory CENTRALLIMITTHEOREM LearningObjectives UnderstandtheconceptoftheCentralLimitTheorem UnderstandtheapplicationoftheCentralLimitTheoremtoincreasetheaccuracyofmeasurements WhydoweCare TheCentralLimitTheoremis thekeytheoreticallinkbetweenthenormaldistributionandsamplingdistributions themeansbywhichalmostanysamplingdistribution nomatterhowirregular canbeapproximatedbyanormaldistributionifthesamplesizeislargeenough IMPROVEMENTROADMAPUsesoftheCentralLimitTheorem CommonUses KEYSTOSUCCESS WHATISTHECENTRALLIMITTHEOREM CentralLimitTheoremForalmostallpopulations thesamplingdistributionofthemeancanbeapproximatedcloselybyanormaldistribution providedthesamplesizeissufficientlylarge WhydoweCare HOWDOESTHISWORK Asyouaveragealargerandlargernumberofsamples youcanseehowtheoriginalsampledpopulationistransformed ANOTHERPRACTICALASPECT DICEEXERCISE Breakinto3teamsTeamonewillbeusing2diceTeamtwowillbeusing4diceTeamthreewillbeusing6diceEachteamwillconduct100throwsoftheirdiceandrecordtheaverageofeachthrow Plotahistogramoftheresultingdata Eachteampresentstheresultsina10minreportout LearningObjectives UnderstandtheconceptoftheCentralLimitTheorem UnderstandtheapplicationoftheCentralLimitTheoremtoincreasetheaccuracyofmeasurements PROCESSCAPABILITYANALYSIS LearningObjectives Understandtherolethatprocesscapabilityanalysisplaysinthesuccessfulcompletionofanimprovementproject Knowhowtoperformaprocesscapabilityanalysis WhydoweCare ProcessCapabilityAnalysisisnecessaryto determinetheareaoffocuswhichwillensuresuccessfulresolutionoftheproject benchmarkaprocesstoenabledemonstratedlevelsofimprovementaftersuccessfulresolutionoftheproject demonstrateimprovementaftersuccessfulresolutionoftheproject