six sigma training(ppt 66)6sigma推行教材.pptx

six sigma training(ppt 66)6sigma推行教材.pptx

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Six-SigmaSix-SigmaTrainingBookTrainingBookDec18,20011BPTLConfidential6推行教材4數据分布2BPTLConfidential6推行教材4NormalExponentialWeibullLognormaltc2fContinuousDistributionsSamplingDistributions數据分布3BPTLConfidential6推行教材Themostwidelyusedmodelforthedistributionofcontinuousrandomvariable.Arisesinthestudyofnumerousphysicalphenomena,suchasthevelocityofmolecules.正態分布正態分布PlotisknownasProbabilityDensityFunctionofX4BPTLConfidential6推行教材4Manynaturalphenomenaandman-madeprocessesareobservedtohavenormaldistributions,orcanbecloselyrepresentedasnormallydistributed.4Forexample,thelengthofamachinedpartisobservedtovaryaboutitsmeandueto:

temperaturedrift,humiditychange,vibrations,cuttinganglevariations,cuttingtoolwear,bearingwear,rotationalspeedvariations,fixturingvariations,rawmaterialchangesandcontaminationlevelchanges4Ifthesesourcesofvariationaresmall,independentandequallylikelytobepositiveornegative,thelengthwillcloselyapproximateanormaldistribution.正態分布正態分布5BPTLConfidential6推行教材4FirstintroducedbyFrenchmathematicianAbrahamDeMoivrein1733.4Madefamousin1809byGermanmathematicianK.F.Gausswhenhealsodevelopedanormaldistributionindependentlyanduseditinhisstudyofastronomy.4Asaresult,itisalsoknownastheGaussiandistribution.4Duringmidtolatenineteenthcentury,manystatisticiansbelievedthatitwas“normal”formostwell-behaveddatatofollowthiscurve.正態分布正態分布-歷程表歷程表KarlFriedrichGauss6BPTLConfidential6推行教材4正態分布易于理解,具有特性,統計學提供了許多基于正態分布的強有力的分析方法來幫助人們做決定.4因此,我們通常會試圖用正態分布去近似模擬其它分布（如可能）或轉化數据以“使”它遵從正態分布.4它是分析過程能力的首選分布形式.正態分布正態分布7BPTLConfidential6推行教材4Anormaldistributioncanbecompletelydescribedbyknowingonlythe:

Mean（）Variance

（2）正態分布的一些特性正態分布的一些特性DistributionOneDistributionTwoDistributionThreeWhatisthedifferencebetweenthe3normaldistributions?

XN（,2）18BPTLConfidential6推行教材ANormal（A,A）BNormal（B,B）ANormal（A,A）BNormal（B,B）ANormal（A,A）BNormal（B,B）WhatisthedifferencebetweenprocessA&Bforeachcase?

正態分布的一些特性正態分布的一些特性9BPTLConfidential6推行教材4Themean,medianandmodeallcoincideatthesamevalue-.Thereisperfectsymmetry.+-MeanMedianMode2Themeanrepresentsthearithmeticaverageofallobservationsinadataset.Ifasetofobservationsisarrangedinanincreasingorderofmagnitude（rankeddata）,themiddlevalueiscalledthemedian.lIfthenumberofobservationsisodd,themedianisthevalueofthemiddlenumber.lIfthenumberofobservationsiseven,thereare2middlenumbers,andthemedianistheaverageofthe2values.Themodeistheobservationthatoccursmostfrequentlyinthesample.正態分布的一些特性正態分布的一些特性10BPTLConfidential6推行教材4Theareaundersectionsofthecurvecanbeusedtoestimatethecumulativeprobabilityofacertain“event”occurring:

PointofInflection1+-68.27%95.45%99.73%+/-3isoftenreferredtoasthewidthofanormaldistribution3正態分布的一些特性正態分布的一些特性11BPTLConfidential6推行教材Letscomputethecumulativeprobabilitiesofthefollowingdistributions:

+-m=3.5s=0.61.8+-20.0=16.6=2.8+-m=-1.5s=0.9-2.80.5正態分布的一些特性正態分布的一些特性12BPTLConfidential6推行教材MiniTab:

CalcProbabilityDistributionsNormal.EntervalueEntersvalueEnterxvalue正態分布的一些特性正態分布的一些特性13BPTLConfidential6推行教材什么是什么是6?

14BPTLConfidential6推行教材6簡介15BPTLConfidential6推行教材TheFocusofSixSigma4Identifyingcriticalaspectsofthebusinesswithproblemsoropportunitiesforimprovement.4TargetingthosecriticalareasanddesignatingimprovementeffortsasSixSigmaBlackBeltprojects.4Selectingtoppeopletoworkontheprojects-fulltime.4Ensuringthesepeoplehavethetime,tools,andresourcestheyneedtosucceed.16BPTLConfidential6推行教材CustomerFocus:

AModelForSuccessTechnologyTechnologyCapabilityCapabilityOrganizationOrganizationPeoplePeopleProcessesProcesses商務上的生存競爭有賴于我們多大程度上讓我們的客戶滿意商務上的生存競爭有賴于我們多大程度上讓我們的客戶滿意.客戶滿意才能体現品質客戶滿意才能体現品質,价格价格,和貨期的意義和貨期的意義.品質品質,成本成本,准時走貨無不依耐于工序能力准時走貨無不依耐于工序能力.WhatpurposeisSix-sigma?

17BPTLConfidential6推行教材SixSigmaVisionTheVisionofSixSigmaistodelightcustomersbydeliveringworld-classqualityproductsthroughtheachievementofSixSigmalevelsofperformanceineverythingwedo.WhatpurposeisSix-sigma?

SixSigmaPhilosophyThephilosophyofSixSigmaistoapplyastructured,systematicapproachtoachievebreakthroughimprovementacrossallareasofourbusiness.18BPTLConfidential6推行教材PPMProcessCapabilityDefectsperMillionOpp.SixSigma-AggressiveGoalWhatpurposeisSix-sigma?

19BPTLConfidential6推行教材StatisticalDefinitionofn-SigmaLSLLSLUSLUSLProcessWidthoDesignWidthTTscaleLSLLSLUSLUSLscaleTT+nscale-nThisistheso-calledn-sigmaSigmaisastatisticalunitofmeasurethatreflectsprocesscapability.Thesigmascaleofmeasureisperfectlycorrelatedtosuchcharacteristicsasdefects-per-unit,parts-permilliondefective,andtheprobabilityofafailure/error.20BPTLConfidential6推行教材StatisticalDefinitionof6Thisisthesix-sigmawesaidLSLLSLUSLUSLProcessWidthoDesignWidth-3st+3stTT.001ppmUSL.001ppm2）b）工序能力可工序能力可（Cp=1to2）c）工序能力差工序能力差（Cp1.5）b）工序能力可工序能力可（Cpk=1to1.5）c）工序能力差工序能力差（Cpk1）a）Cp=2Cpk=2b）Cp=2Cpk=1c）Cp=2Cpk143BPTLConfidential6推行教材工序潛力与工序表現工序潛力与工序表現（a）PoorProcessPotential（b）PoorProcessPerformanceLSLUSLLSLUSLExperimentalDesigntoreducevariationExperimentalDesigntocentermeantoreducevariation44BPTLConfidential6推行教材工序潛力与工序表現工序潛力与工序表現a）Cp=2Cpk=2b）Cp=2Cpk=1c）Cp=2Cpk145BPTLConfidential6推行教材工序穩定性工序穩定性Aprocessisstableifthedistributionofmeasurementsmadeonthegivenfeatureisconsistentovertime.TimeStableProcessTimeUnstableProcessucllclucllcl46BPTLConfidential6推行教材短期工序能力与長期工序能力短期工序能力与長期工序能力短期工序能力短期工序能力（previouslycalledshort-termcapability）showstheinherentvariabilityofamachine/processoperatingwithinabriefperiodoftime.長期工序能力長期工序能力（previouslycalledlong-termcapability）showsthevariabilityofamachine/processoperatingoveraperiodoftime.Itincludessourcesofvariationinadditiontotheshort-termvariability.47BPTLConfidential6推行教材WithinOverallSampleSize3050units100unitsNumberofLotssinglelotseverallotsPeriodofTimehoursordaysweeksormonthsNumberofOperatorssingleoperatordifferentoperatorsProcessPotentialCpPpProcessPerformanceCpkPpk短期工序能力与長期工序能力短期工序能力与長期工序能力48BPTLConfidential6推行教材實戰演練實戰演練Thelengthofacamshaftforanautomobileengineisspecifiedat6002mm.Controlofthelengthofthecamshaftiscriticaltoavoidscrap/rework.Thecamshaftisprovidedbyexternalsuppliers.Assesstheprocesscapabilityforthissupplier.ThedataisavailableinCamshaft.MTW.Dataarecollectedinsubgroupsof5each.49BPTLConfidential6推行教材Example4Minitab:

StatQualityToolsCapabilityAnalysis（Normal）50BPTLConfidential6推行教材Example451BPTLConfidential6推行教材Example5Histogramofthecamshaftlengthsuggestsmixedpopulations.Furtherinvestigationrevealedthattherearetwosuppliersforthecamshaft.Datawerenowcollectedoncamshaftsfromeachsourcewithoutcombiningboth.Subgroupsizeis5foreachsupplier.Arethetwosupplierssimilarinperformance?

Ifnot,whatareyourrecommendations?

52BPTLConfidential6推行教材Example5MiniTab:

StatQualityToolsCapabilitySixpack（Normal）53BPTLConfidential6推行教材Example554BPTLConfidential6推行教材Example555BPTLConfidential6推行教材用用Box-Cox轉化后的工序能力分析轉化后的工序能力分析4Whentheprocessdataarenotnormal,theCpkorPpkindicesarenotaccurateorreliable,becausetheseindicesarecomputedonthebasisthatthedataarenormallydistributed.4Dppmvaluesassociatedwiththeindiceswillnotbeneartotheactualperformancewhenthenormalcurvedoesnotmodeltheactualdatawell.56BPTLConfidential6推行教材4Iftheprocessdataaresomewhatbell-shapedbutskewed,Box-Coxtransformationcanbeusedtomakethedatanormalbeforeweassesstheprocesscapability.4RemembertotransformthespecificationlimitstoobeforewecomputeCpkorPpk!

用用Box-Cox轉化后的工序能力分析轉化后的工序能力分析57BPTLConfidential6推行教材Minitab:

StatQualityToolsCapabilityAnalysis（Normal）用用Box-Cox轉化后的工序能力分析轉化后的工序能力分析58BPTLConfidential6推行教材Example6OpenthefilenamedDimension.MTWintheDay-2folderagain.Computetheprocesscapabilitywiththespecificationlimits:

LSL:

0.1USL:

10Arethedatanormallydistributed?

ComputetheprocesscapabilityagainwithBox-Coxtransformation.用用Box-Cox轉化后的工序能力分析轉化后的工序能力分析59BPTLConfidential6推行教材Cpkof0.41isreportedintheSSATpackage.Thisvalueisnotreliableoraccurateifthedataarenotnormal.DataisnotnormalExample6用用Box-Cox轉化后的工序能力分析轉化后的工序能力分析60BPTLConfidential6推行教材Example6Cpkhasincreasedfrom0.41to0.81用用Box-Cox轉化后的工序能力分析轉化后的工序能力分析61BPTLConfidential6推行教材Whats“6”QualityThen4OriginalDefinitionbyMotorola:

4Intheshortterm,thespecificationlimitsareatleast6awayfromtheprocessmean,i.e.Cp2,4Inthelongrun,theprocesswillshiftbylessthan1.5,i.e.Ppk1.5,4Theprocesswillyieldlessthan3.4dppmrejectedparts.66Shift1.54.5“SigmaLevel”Capability62BPTLConfidential6推行教材WhatsSixSigmaQualityNowMikelJHarryclaimsthattheprocessmeanbetweenlotswillvary,withanaverageprocessshiftof1.5.k=z+1.5k=z+1.5Shift1.5zNote:

SigmaCapability=（dpmo）（dppm）“SigmaLevel”Capability63BPTLConfidential6推行教材TypesofVariation1.PositionalVariationSameprocess,variationatdifferinglocationssimultaneously:

TemperaturevariationsinsideathermalchamberCavity-to-cavityvariationsinaninjectionmold2.CyclicalVariationSequentialrepetitionsofaprocessoverfairlyshorttime,say,lessthan15mins:

VariationsbetweenconsecutivebatchesofaprocessDifferencesfromlottolotofrawmaterials64BPTLConfidential6推行教材TypesofVariation3.TemporalVariationVariationsoverlongerperiodsoftime,suchaseveralhours,daysorweeks.65BPTLConfidential6推行教材MeasurementSystemAnalysisApproachTherearetwotypesofmeasurementspossible:

4VariableDatacanbedescribedonacontinuousscale4Attribut