QSM754

SIXSIGMAAPPLICATIONSAGENDA第一頁，共二百六十三頁。Day1AgendaWelcomeandIntroductions CourseStructure MeetingGuidelines/CourseAgenda/ReportOutCriteriaGroupExpectations IntroductiontoSixSigmaApplicationsRedBeadExperimentIntroductiontoProbabilityDistributionsCommonProbabilityDistributionsandTheirUsesCorrelationAnalysis第二頁，共二百六十三頁。Day2AgendaTeamReportOutsonDay1Material CentralLimitTheoremProcessCapabilityMulti-VariAnalysisSampleSizeConsiderations第三頁，共二百六十三頁。Day3AgendaTeamReportOutsonDay2Material ConfidenceIntervalsControlChartsHypothesisTestingANOVA(AnalysisofVariation)ContingencyTables第四頁，共二百六十三頁。Day4AgendaTeamReportOutsonPracticumApplication DesignofExperimentsWrapUp-PositivesandDeltas第五頁，共二百六十三頁。ClassGuidelinesQ&Aaswego BreaksHourlyHomeworkReadingsAsassignedinSyllabusGradingClassPreparation 30%TeamClassroomExercises 30%TeamPresentations 40%10MinuteDailyPresentation(Day2and3)onApplicationofpreviousdayswork20minutefinalPracticumapplication(Lastday)CopyonFloppyaswellashardcopyPowerpointpreferredRotatePresentersQ&Afromtheclass第六頁，共二百六十三頁。INTRODUCTIONTOSIXSIGMAAPPLICATIONS第七頁，共二百六十三頁。LearningObjectivesHaveabroadunderstandingofstatisticalconceptsandtools.Understandhowstatisticalconceptscanbeusedtoimprovebusinessprocesses.Understandtherelationshipbetweenthecurriculumandthefourstepsixsigmaproblemsolvingprocess(Measure,Analyze,ImproveandControl).第八頁，共二百六十三頁。WhatisSixSigma?APhilosophyAQualityLevelAStructuredProblem-SolvingApproachAProgramCustomerCriticalToQuality(CTQ)CriteriaBreakthroughImprovementsFact-driven,Measurement-based,StatisticallyAnalyzedPrioritizationControllingtheInput&ProcessVariationsYieldsaPredictableProduct6s=3.4DefectsperMillionOpportunitiesPhasedProject: Measure,Analyze,Improve,ControlDedicated,TrainedBlackBeltsPrioritizedProjectsTeams-ProcessParticipants&Owners第九頁，共二百六十三頁。POSITIONINGSIXSIGMA

THEFRUITOFSIXSIGMAGroundFruitLogicandIntuitionLowHangingFruitSevenBasicToolsBulkofFruitProcessCharacterizationandOptimizationProcess

EntitlementSweetFruit

DesignforManufacturability第十頁，共二百六十三頁。UNLOCKINGTHEHIDDENFACTORYVALUESTREAMTOTHECUSTOMERPROCESSESWHICHPROVIDEPRODUCTVALUEINTHECUSTOMER’SEYESFEATURESORCHARACTERISTICSTHECUSTOMERWOULDPAYFOR….WASTEDUETOINCAPABLEPROCESSESWASTESCATTEREDTHROUGHOUTTHEVALUESTREAMEXCESSINVENTORYREWORKWAITTIMEEXCESSHANDLINGEXCESSTRAVELDISTANCESTESTANDINSPECTIONWasteisasignificantcostdriverandhasamajorimpactonthebottomline...第十一頁，共二百六十三頁。CommonSixSigmaProjectAreasManufacturingDefectReductionCycleTimeReductionCostReductionInventoryReductionProductDevelopmentandIntroductionLaborReductionIncreasedUtilizationofResourcesProductSalesImprovementCapacityImprovementsDeliveryImprovements第十二頁，共二百六十三頁。TheFocusofSixSigma…..Y=f(x)Allcriticalcharacteristics(Y)aredrivenbyfactors(x)whichare“upstream”fromtheresults….Attemptingtomanageresults(Y)onlycausesincreasedcostsduetorework,testandinspection…Understandingandcontrollingthecausativefactors(x)istherealkeytohighqualityatlowcost...第十三頁，共二百六十三頁。INSPECTIONEXERCISEThenecessityoftrainingfarmhandsforfirstclassfarmsinthefatherlyhandlingoffarmlivestockisforemostinthemindsoffarmowners.Sincetheforefathersofthefarmownerstrainedthefarmhandsforfirstclassfarmsinthefatherlyhandlingoffarmlivestock,thefarmownersfeeltheyshouldcarryonwiththefamilytraditionoftrainingfarmhandsoffirstclassfarmsinthefatherlyhandlingoffarmlivestockbecausetheybelieveitisthebasisofgoodfundamentalfarmmanagement.Howmanyf’scanyouidentifyin1minuteofinspection….第十四頁，共二百六十三頁。INSPECTIONEXERCISEThenecessityof*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.第十五頁，共二百六十三頁。SIXSIGMACOMPARISONSixSigmaTraditional“SIXSIGMATAKESUSFROMFIXINGPRODUCTSSOTHEYAREEXCELLENT,TOFIXINGPROCESSESSOTHEYPRODUCEEXCELLENTPRODUCTS”

Dr.GeorgeSarney,President,SiebeControlSystems第十六頁，共二百六十三頁。IMPROVEMENTROADMAPBreakthroughStrategyCharacterizationPhase

1:MeasurementPhase2:AnalysisOptimizationPhase3:ImprovementPhase

4:ControlDefinetheproblemandverifytheprimaryandsecondarymeasurementsystems.Identifythefewfactorswhicharedirectlyinfluencingtheproblem.Determinevaluesforthefewcontributingfactorswhichresolvetheproblem.Determinelongtermcontrolmeasureswhichwillensurethatthecontributingfactorsremaincontrolled.Objective第十七頁，共二百六十三頁。Measurementsarecritical...Ifwecan’taccuratelymeasuresomething,wereallydon’tknowmuchaboutit.Ifwedon’tknowmuchaboutit,wecan’tcontrolit.Ifwecan’tcontrolit,weareatthemercyofchance.第十八頁，共二百六十三頁。WHYSTATISTICS?

THEROLEOFSTATISTICSINSIXSIGMA..WEDON’TKNOWWHATWEDON’TKNOWIFWEDON’THAVEDATA,WEDON’TKNOWIFWEDON’TKNOW,WECANNOTACTIFWECANNOTACT,THERISKISHIGHIFWEDOKNOWANDACT,THERISKISMANAGEDIFWEDOKNOWANDDONOTACT,WEDESERVETHELOSS.

DR.MikelJ.HarryTOGETDATAWEMUSTMEASUREDATAMUSTBECONVERTEDTOINFORMATIONINFORMATIONISDERIVEDFROMDATATHROUGHSTATISTICS第十九頁，共二百六十三頁。WHYSTATISTICS?

THEROLEOFSTATISTICSINSIXSIGMA..Ignoranceisnotbliss,itisthefoodoffailureandthebreedinggroundforloss. DR.MikelJ.HarryYearsagoastatisticianmighthaveclaimedthatstatisticsdealtwiththeprocessingofdata….Today’sstatisticianwillbemorelikelytosaythatstatisticsisconcernedwithdecisionmakinginthefaceofuncertainty. Bartlett第二十頁，共二百六十三頁。SalesReceiptsOnTimeDeliveryProcessCapacityOrderFulfillmentTimeReductionofWasteProductDevelopmentTimeProcessYieldsScrapReductionInventoryReductionFloorSpaceUtilizationWHATDOESITMEAN?RandomChanceorCertainty….Whichwouldyouchoose….?第二十一頁，共二百六十三頁。LearningObjectivesHaveabroadunderstandingofstatisticalconceptsandtools.Understandhowstatisticalconceptscanbeusedtoimprovebusinessprocesses.Understandtherelationshipbetweenthecurriculumandthefourstepsixsigmaproblemsolvingprocess(Measure,Analyze,ImproveandControl).第二十二頁，共二百六十三頁。REDBEADEXPERIMENT第二十三頁，共二百六十三頁。LearningObjectivesHaveanunderstandingofthedifferencebetweenrandomvariationandastatisticallysignificantevent.Understandthedifferencebetweenattemptingtomanageanoutcome(Y)asopposedtomanagingupstreameffects(x’s).Understandhowtheconceptofstatisticalsignificancecanbeusedtoimprovebusinessprocesses.第二十四頁，共二百六十三頁。WELCOMETOTHEWHITEBEADFACTORYHIRINGNEEDSBEADSAREOURBUSINESSPRODUCTIONSUPERVISOR4PRODUCTIONWORKERS2INSPECTORS1INSPECTIONSUPERVISOR1TALLYKEEPER第二十五頁，共二百六十三頁。STANDINGORDERSFollowtheprocessexactly.Donotimproviseorvaryfromthedocumentedprocess.Yourperformancewillbebasedsolelyonyourabilitytoproducewhitebeads.Noquestionswillbeallowedaftertheinitialtrainingperiod.Yourdefectquotaisnomorethan5offcolorbeadsallowedperpaddle.第二十六頁，共二百六十三頁。WHITEBEADMANUFACTURINGPROCESSPROCEDURESTheoperatorwilltakethebeadpaddleintherighthand.Insertthebeadpaddleata45degreeangleintothebeadbowl.Agitatethebeadpaddlegentlyinthebeadbowluntilallspacesarefilled.Gentlywithdrawthebeadpaddlefromthebowlata45degreeangleandallowthefreebeadstorunoff.Withouttouchingthebeads,showthepaddletoinspector#1andwaituntiltheoffcolorbeadsaretallied.Movetoinspector#2andwaituntiltheoffcolorbeadsaretallied.Inspector#1and#2showtheirtalliestotheinspectionsupervisor.Iftheyagree,theinspectionsupervisorannouncesthecountandthetallykeeperwillrecordtheresult.Iftheydonotagree,theinspectionsupervisorwilldirecttheinspectorstorecountthepaddle.Whenthecountiscomplete,theoperatorwillreturnallthebeadstothebowlandhandthepaddletothenextoperator.第二十七頁，共二百六十三頁。INCENTIVEPROGRAMLowbeadcountswillberewardedwithabonus.Highbeadcountswillbepunishedwithareprimand.Yourperformancewillbebasedsolelyonyourabilitytoproducewhitebeads.Yourdefectquotaisnomorethan7offcolorbeadsallowedperpaddle.第二十八頁，共二百六十三頁。PLANTRESTRUCTUREDefectcountsremaintoohighfortheplanttobeprofitable.Thetwobestperformingproductionworkerswillberetainedandthetwoworstperformingproductionworkerswillbelaidoff.Yourperformancewillbebasedsolelyonyourabilitytoproducewhitebeads.Yourdefectquotaisnomorethan10offcolorbeadsallowedperpaddle.第二十九頁，共二百六十三頁。OBSERVATIONS…….WHATOBSERVATIONSDIDYOUMAKEABOUTTHISPROCESS….?第三十頁，共二百六十三頁。TheFocusofSixSigma…..Y=f(x)Allcriticalcharacteristics(Y)aredrivenbyfactors(x)whichare“downstream”fromtheresults….Attemptingtomanageresults(Y)onlycausesincreasedcostsduetorework,testandinspection…Understandingandcontrollingthecausativefactors(x)istherealkeytohighqualityatlowcost...第三十一頁，共二百六十三頁。LearningObjectivesHaveanunderstandingofthedifferencebetweenrandomvariationandastatisticallysignificantevent.Understandthedifferencebetweenattemptingtomanageanoutcome(Y)asopposedtomanagingupstreameffects(x’s).Understandhowtheconceptofstatisticalsignificancecanbeusedtoimprovebusinessprocesses.第三十二頁，共二百六十三頁。INTRODUCTIONTOPROBABILITYDISTRIBUTIONS第三十三頁，共二百六十三頁。LearningObjectivesHaveabroadunderstandingofwhatprobabilitydistributionsareandwhytheyareimportant.Understandtherolethatprobabilitydistributionsplayindeterminingwhetheraneventisarandomoccurrenceorsignificantlydifferent.Understandthecommonmeasuresusedtocharacterizeapopulationcentraltendencyanddispersion.UnderstandtheconceptofShift&Drift.Understandtheconceptofsignificancetesting.第三十四頁，共二百六十三頁。WhydoweCare?AnunderstandingofProbabilityDistributionsisnecessaryto:

Understandtheconceptanduseofstatisticaltools.Understandthesignificanceofrandomvariationineverydaymeasures.Understandtheimpactofsignificanceonthesuccessfulresolutionofaproject.第三十五頁，共二百六十三頁。IMPROVEMENTROADMAP

UsesofProbabilityDistributionsBreakthroughStrategyCharacterizationPhase

1:MeasurementPhase2:AnalysisOptimizationPhase3:ImprovementPhase

4:ControlEstablishbaselinedatacharacteristics.ProjectUsesIdentifyandisolatesourcesofvariation.Usetheconceptofshift&drifttoestablishprojectexpectations.Demonstratebeforeandafterresultsarenotrandomchance.第三十六頁，共二百六十三頁。FocusonunderstandingtheconceptsVisualizetheconceptDon’tgetlostinthemath….KEYSTOSUCCESS第三十七頁，共二百六十三頁。Measurementsarecritical...Ifwecan’taccuratelymeasuresomething,wereallydon’tknowmuchaboutit.Ifwedon’tknowmuchaboutit,wecan’tcontrolit.Ifwecan’tcontrolit,weareatthemercyofchance.第三十八頁，共二百六十三頁。TypesofMeasuresMeasureswherethemetriciscomposedofaclassificationinoneoftwo(ormore)categoriesiscalledAttributedata.Thisdataisusuallypresentedasa“count”or“percent”.Good/BadYes/NoHit/Missetc.MeasureswherethemetricconsistsofanumberwhichindicatesaprecisevalueiscalledVariabledata.TimeMiles/Hr第三十九頁，共二百六十三頁。COINTOSSEXAMPLETakeacoinfromyourpocketandtossit200times.Keeptrackofthenumberoftimesthecoinfallsas“heads”.Whencomplete,theinstructorwillaskyouforyour“head”count.第四十頁，共二百六十三頁。COINTOSSEXAMPLE1301201101009080701000050000Cumulative

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PercentCumulativeFrequencyCumulativePercentCumulativecountissimplythetotalfrequencycountaccumulatedasyoumovefromlefttorightuntilweaccountforthetotalpopulationof10,000people.Sinceweknowhowmanypeoplewereinthispopulation(ie10,000),wecandivideeachofthecumulativecountsby10,000togiveusacurvewiththecumulativepercentofpopulation.第四十一頁，共二百六十三頁。COINTOSSPROBABILITYEXAMPLE130120110100908070100500Cumulative

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PercentThismeansthatwecannowpredictthechangethatcertainvaluescanoccurbasedonthesepercentages.Noteherethat50%ofthevaluesarelessthanourexpectedvalueof100.Thismeansthatinafutureexperimentsetupthesameway,wewouldexpect50%ofthevaluestobelessthan100.第四十二頁，共二百六十三頁。COINTOSSEXAMPLE1301201101009080706005004003002001000"Head

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PercentWecannowequateaprobabilitytotheoccurrenceofspecificvaluesorgroupsofvalues.Forexample,wecanseethattheoccurrenceofa“Headcount”oflessthan74orgreaterthan124outof200tossesissorarethatasingleoccurrencewasnotregisteredoutof10,000tries.Ontheotherhand,wecanseethatthechanceofgettingacountnear(orat)100ismuchhigher.Withthedatathatwenowhave,wecanactuallypredicteachofthesevalues.第四十三頁，共二百六十三頁。COINTOSSPROBABILITYDISTRIBUTION-6-5-4-3-2-10123456NUMBEROFHEADSPROCESSCENTEREDONEXPECTEDVALUEsSIGMA(s)ISAMEASUREOF“SCATTER”FROMTHEEXPECTEDVALUETHATCANBEUSEDTOCALCULATEAPROBABILITYOFOCCURRENCESIGMAVALUE(Z)CUM%OFPOPULATION586572798693100107114121128135142.003.1352.27515.8750.084.197.799.8699.9971301201101009080706005004003002001000FrequencyIfweknowwhereweareinthepopulationwecanequatethattoaprobabilityvalue.Thisisthepurposeofthesigmavalue(normaldata).%ofpopulation=probabilityofoccurrence第四十四頁，共二百六十三頁。CommonOccurrenceRareEventWHATDOESITMEAN?Whatarethechancesthatthis“justhappened”Iftheyaresmall,chancesarethatanexternalinfluenceisatworkthatcanbeusedtoourbenefit….第四十五頁，共二百六十三頁。ProbabilityandStatistics“theoddsofColoradoUniversitywinningthenationaltitleare3to1”“DrewBledsoe’spasscompletionpercentageforthelast6gamesis.58%versus.78%forthefirst5games”“TheSenatorwillwintheelectionwith54%ofthepopularvotewithamarginof+/-3%”

ProbabilityandStatisticsinfluenceourlivesdailyStatisticsistheuniversallanuageforscienceStatisticsistheartofcollecting,classifying,presenting,interpretingandanalyzingnumericaldata,aswellasmakingconclusionsaboutthesystemfromwhichthedatawasobtained.第四十六頁，共二百六十三頁。PopulationVs.Sample(CertaintyVs.Uncertainty)

Asampleisjustasubsetofallpossiblevaluespopulationsample

Sincethesampledoesnotcontainallthepossiblevalues,thereissomeuncertaintyaboutthepopulation.Henceanystatistics,suchasmeanandstandarddeviation,arejustestimatesofthetruepopulationparameters.第四十七頁，共二百六十三頁。DescriptiveStatisticsDescriptiveStatisticsisthebranchofstatisticswhichmostpeoplearefamiliar.Itcharacterizesandsummarizesthemostprominentfeaturesofagivensetofdata(means,medians,standarddeviations,percentiles,graphs,tablesandcharts.DescriptiveStatisticsdescribetheelementsofapopulationasawholeortodescribedatathatrepresentjustasampleofelementsfromtheentirepopulationInferentialStatistics第四十八頁，共二百六十三頁。InferentialStatisticsInferentialStatisticsisthebranchofstatisticsthatdealswithdrawingconclusionsaboutapopulationbasedoninformationobtainedfromasampledrawnfromthatpopulation.Whiledescriptivestatisticshasbeentaughtforcenturies,inferentialstatisticsisarelativelynewphenomenonhavingitsrootsinthe20thcentury.We“infer”somethingaboutapopulationwhenonlyinformationfromasampleisknown.ProbabilityisthelinkbetweenDescriptiveandInferentialStatistics第四十九頁，共二百六十三頁。WHATDOESITMEAN?-6-5-4-3-2-10123456NUMBEROFHEADSsSIGMAVALUE(Z)CUM%OFPOPULATION586572798693100107114121128135142.003.1352.27515.8750.084.197.799.8699.9971301201101009080706005004003002001000FrequencyAndthefirst50trialsshowed“HeadCounts”greaterthan130?WHATIFWEMADEACHANGETOTHEPROCESS?Chancesareverygoodthattheprocessdistributionhaschanged.Infact,thereisaprobabilitygreaterthan99.999%thatithaschanged.第五十頁，共二百六十三頁。USESOFPROBABILITYDISTRIBUTIONSCriticalValueCriticalValueCommonOccurrenceRareOccurrenceRareOccurrencePrimarilythesedistributionsareusedtotestforsignificantdifferencesindatasets.Tobeclassifiedassignificant,theactualmeasuredvaluemustexceedacriticalvalue.Thecriticalvalueistabularvaluedeterminedbytheprobabilitydistributionandtheriskoferror.Thisriskoferroriscalledariskandindicatestheprobabilityofthisvalueoccurringnaturally.So,anariskof.05(5%)meansthatthiscriticalvaluewillbeexceededbyarandomoccurrencelessthan5%ofthetime.第五十一頁，共二百六十三頁。SOWHATMAKESADISTRIBUTIONUNIQUE?CENTRALTENDENCYWhereapopulationislocated.DISPERSIONHowwideapopulationisspread.DISTRIBUTIONFUNCTIONThemathematicalformulathatbestdescribesthedata(wewillcoverthisindetailinthenextmodule).第五十二頁，共二百六十三頁。COINTOSSCENTRALTENDENCY1301201101009080706005004003002001000NumberofoccurrencesWhataresomeofthewaysthatwecaneasilyindicatethecenteringcharacteristicofthepopulation?Threemeasureshavehistoricallybeenused;themean,themedianandthemode.

第五十三頁，共二百六十三頁。WHATISTHEMEAN?ORDEREDDATASET-5-3-1-10000013-6-5-4-3-2-101234564Themeanhasalreadybeenusedinseveralearliermodulesandisthemostcommonmeasureofcentraltendencyforapopulation.Themeanissimplytheaveragevalueofthedata.n=12xi=-?2meanxxni===-=-?21217.Mean第五十四頁，共二百六十三頁。WHATISTHEMEDIAN?ORDEREDDATASET-5-3-1-10000013-6-5-4-3-2-101234564Ifwerankorder(descendingorascending)thedatasetforthisdistributionwecouldrepresentcentraltendencybytheorderofthedatapoints.Ifwefindthevaluehalfway(50%)throughthedatapoints,wehaveanotherwayofrepresentingcentraltendency.Thisiscalledthemedianvalue.MedianValueMedian50%ofdatapoints第五十五頁，共二百六十三頁。WHATISTHEMODE?ORDEREDDATASET-5-3-1-10000013-6-5-4-3-2-101234564Ifwerankorder(descendingorascending)thedatasetforthisdistributionwefindseveralwayswecanrepresentcentraltendency.Wefindthatasinglevalueoccursmoreoftenthananyother.Sinceweknowthatthereisahigherchanceofthisoccurrenceinthemiddleofthedistribution,wecanusethisfeatureasanindicatorofcentraltendency.Thisiscalledthemode.ModeMode第五十六頁，共二百六十三頁。MEASURESOFCENTRALTENDENCY,SUMMARYMEAN()(Otherwiseknownastheaverage)XXni==-=?21217.XORDEREDDATASET-5-3-1-10000013-6-5-4-3-2-101234564ORDEREDDATASET-5-3-1-10000013-6-5-4-3-2-101234564ORDEREDDATASET-5-3-1-10000013-6-5-4-3-2-101234564MEDIAN(50percentiledatapoint)Herethemedianvaluefallsbetweentwozerovaluesandthereforeiszero.Ifthevaluesweresay2and3instead,themedianwouldbe2.5.MODE

(Mostcommonvalueinthedataset)Themodeinthiscaseis0with5occurrenceswithinthisdata.Mediann=12n/2=6n/2=6}Mode=0Mode=0第五十七頁，共二百六十三頁。SOWHAT’STHEREALDIFFERENCE?MEANThemeanisthemostconsistentlyaccuratemeasureofcentraltendency,butismoredifficulttocalculatethantheothermeasures.MEDIANANDMODEThemedianandmodearebothveryeasytodetermine.That’sthegoodnews….Thebadnewsisthatbotharemoresusceptibletobiasthanthemean.第五十八頁，共二百六十三頁。SOWHAT’STHEBOTTOMLINE?MEANUseonalloccasionsunlessacircumstanceprohibitsitsuse.MEDIANANDMODEOnlyuseifyoucannotusemean.第五十九頁，共二百六十三頁。COINTOSSPOPULATIONDISPERSION1301201101009080706005004003002001000NumberofoccurrencesWhataresomeofthewaysthatwecaneasilyindicatethedispersion(spread)characteristicofthepopulation?Threemeasureshavehistoricallybeenused;therange,thestandarddeviationandthevariance.

第六十頁，共二百六十三頁。WHATISTHERANGE?ORDEREDDATASET-5-3-1-10000013-6-5-4-3-2-101234564Therangeisaverycommonmetricwhichiseasilydeterminedfromanyorderedsample.Tocalculatetherangesimplysubtracttheminimumvalueinthesamplefromthemaximumvalue.RangeRangeMaxMinRangexxMAXMIN=-=--=459()第六十一頁，共二百六十三頁。WHATISTHEVARIANCE/STANDARDDEVIATION?Thevariance(s2)isaveryrobustmetricwhichrequiresafairamountofworktodetermine.Thestandarddeviation(s)isthesquarerootofthevarianceandisthemostcommonlyusedmeasureofdispersionforlargersamplesizes.()sXXni221616712156=--=-=?..DATASET-5-3-1-10000013-6-5-4-3-2-101234564XXni==-=?212-.17XXi--5-(-.17)=-4.83-3-(-.17)=-2.83-1-(-.17)=-.83-1-(-.17)=-.830-(-.17)=.170-(-.17)=.170-(-.17)=.170-(-.17)=.170-(-.17)=.171-(-.17)=1.173-(-.17)=3.174-(-.17)=4.17(-4.83)2=23.32(-2.83)2=8.01(-.83)2=.69(-.83)2=.69(.17)2=.03(.17)2=.03(.17)2=.03(.17)2=.03(.17)2=.03(1.17)2=1.37(3.17)2=10.05(4.17)2=17.3961.67第六十二頁，共二百六十三頁。MEASURESOFDISPERSIONRANGE(R)(Themaximumdatavalueminustheminimum)ORDEREDDATASET-5-3-1-10000013-6-5-4-3-2-101234564ORDEREDDATASET-5-3-1-10000013-6-5-4-3-2-101234564VARIANCE(s2)(Squareddeviationsaroundthecenterpoint)STANDARDDEVIATION(s)

(Absolutedeviationaroundthecenterpoint)Min=-5RXX=-=--=maxmin()4610Max=4DATASET-5-3-1-10000013-6-5-4-3-2-101234564XXni==-=?212-.17()sXXni221616712156=--=-=?..XXi--5-(-.17)=-4.83-3-(-.17)=-2.83-1-(-.17)=-.83-1-(-.17)=-.830-(-.17)=.170-(-.17)=.170-(-.17)=.170-(-.17)=.170-(-.17)=.171-(-.17)=1.173-(-.17)=3.174-(-.17)=4.17(-4.83)2=23.32(-2.83)2=8.01(-.83)2=.69(-.83)2=.69(.17)2=.03(.17)2=.03(.17)2=.03(.17)2=.03(.17)2=.03(1.17)2=1.37(3.17)2=10.05(4.17)2=17.3961.67ss===256237..第六十三頁，共二百六十三頁。SAMPLEMEANANDVARIANCEEXAMPLE$m==?XNXis()$221==-?2sn-XXiXi1015

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101212345678910SXXi-XXi()2-XXi2s第六十四頁，共二百六十三頁。SOWHAT’STHEREALDIFFERENCE?VARIANCE/STANDARDDEVIATIONThestandarddeviationisthemostconsistentlyaccuratemeasureofcentraltendencyforasinglepopulation.Thevariancehastheaddedbenefitofbeingadditiveovermultiplepopulations.Botharedifficultandtimeconsumingtocalculate.RANGETherangeisveryeasytodetermine.That’sthegoodnews….Thebadnewsisthatitisverysusceptibletobias.第六十五頁，共二百六十三頁。SOWHAT’STHEBOTTOMLINE?VARIANCE/STANDARDDEVIATIONBestusedwhenyouhaveenoughsamples(>10).RANGEGoodforsmallsamples(10orless).第六十六頁，共二百六十三頁。SOWHATISTHISSHIFT&DRIFTSTUFF...Theprojectisprogressingwellandyouwrapitup.6monthslateryouaresurprisedtofindthatthepopulationhastakenashift.-12-10-8-6-4-2024681012

USLLSL第六十七頁，共二百六十三頁。SOWHATHAPPENED?Allofourworkwasfocusedinanarrowtimeframe.Overtime,otherlongterminfluencescomeandgowhichmovethepopulationandchangesomeofitscharacteristics.Thisiscalledshiftanddrift.TimeHistorically,thisshiftanddriftprimarilyimpactsthepositionofthemeanandshiftsit1.5sfromit’soriginalposition.OriginalStudy第六十八頁，共二百六十三頁。VARIATIONFAMILIESVariationispresentuponrepeatmeasurementswithinthesamesample.Variationispresentuponmeasurementsofdifferentsamplescollectedwithinashorttimeframe.Variationispresentuponmeasurementscollectedwithasignificantamountoftimebetweensamples.SourcesofVariationWithinIndividualSamplePiecetoPieceTimetoTime第六十九頁，共二百六十三頁。SOWHATDOESITMEAN?Tocompensatefortheselongtermvariations,wemustconsidertwosetsofmetri