TrainingSix-Sigma

Dec18,2001BPTLConfidential1Six-SigmaTrainingBook6σ推行教材BPTLConfidential2數据分布6σ推行教材BPTLConfidential3NormalExponentialWeibullLognormaltc2fContinuousDistributionsSamplingDistributions數据分布6σ推行教材BPTLConfidential4Themostwidelyusedmodelforthedistributionofcontinuousrandomvariable.Arisesinthestudyofnumerousphysicalphenomena,suchasthevelocityofmolecules.正態分布xe21xf2x21σμπσPlotisknownasProbabilityDensityFunctionofX6σ推行教材BPTLConfidential5Manynaturalphenomenaandman-madeprocessesareobservedtohavenormaldistributions,orcanbecloselyrepresentedasnormallydistributed.Forexample,thelengthofamachinedpartisobservedtovaryaboutitsmeandueto:temperaturedrift,humiditychange,vibrations,cuttinganglevariations,cuttingtoolwear,bearingwear,rotationalspeedvariations,fixturingvariations,rawmaterialchangesandcontaminationlevelchangesIfthesesourcesofvariationaresmall,independentandequallylikelytobepositiveornegative,thelengthwillcloselyapproximateanormaldistribution.正態分布6σ推行教材BPTLConfidential6FirstintroducedbyFrenchmathematicianAbrahamDeMoivrein1733.Madefamousin1809byGermanmathematicianK.F.Gausswhenhealsodevelopedanormaldistributionindependentlyanduseditinhisstudyofastronomy.Asaresult,itisalsoknownastheGaussiandistribution.Duringmidtolatenineteenthcentury,manystatisticiansbelievedthatitwas“normal”formostwell-behaveddatatofollowthiscurve.正態分布-歷程表KarlFriedrichGauss6σ推行教材BPTLConfidential7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.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.它是分析過程能力的首選分布形式.正態分布Anormaldistributioncanbecompletelydescribedbyknowingonlythe:Mean(m)Variance(s2)正態分布的一些特性DistributionOneDistributionTwoDistributionThreeWhatisthedifferencebetweenthe3normaldistributions?xe21xf2x21σμπσX~N(m,s2)16σ推行教材BPTLConfidential9A~Normal(mA,sA²)B~Normal(mB,sB²)A~Normal(mA,sA²)B~Normal(mB,sB²)A~Normal(mA,sA²)B~Normal(mB,sB²)WhatisthedifferencebetweenprocessA&Bforeachcase?正態分布的一些特性6σ推行教材BPTLConfidential10Themean,medianandmodeallcoincideatthesamevalue-m.Thereisperfectsymmetry.µ+-MeanMedianMode2Themeanrepresentsthearithmeticaverageofallobservationsinadataset.Ifasetofobservationsisarrangedinanincreasingorderofmagnitude(rankeddata),themiddlevalueiscalledthemedian.Ifthenumberofobservationsisodd,themedianisthevalueofthemiddlenumber.Ifthenumberofobservationsiseven,thereare2middlenumbers,andthemedianistheaverageofthe2values.Themodeistheobservationthatoccursmostfrequentlyinthesample.正態分布的一些特性Theareaundersectionsofthecurvecanbeusedtoestimatethecumulativeprobabilityofacertain“event”occurring:µPointofInflection1s+-68.27%95.45%99.73%m+/-3sisoftenreferredtoasthewidthofanormaldistribution3正態分布的一些特性6σ推行教材BPTLConfidential12Let’scomputethecumulativeprobabilitiesofthefollowingdistributions:+-m=3.5s=0.61.8+-20.0m=16.6s=2.8+-m=-1.5s=0.9-2.80.5正態分布的一些特性6σ推行教材BPTLConfidential13MiniTab:CalcProbabilityDistributionsNormal...EntermvalueEntersvalueEnterxvalue正態分布的一些特性σ???6σ推行教材BPTLConfidential156σ簡介6σ推行教材BPTLConfidential16TheFocusofSixSigmaIdentifyingcriticalaspectsofthebusinesswithproblemsoropportunitiesforimprovement.TargetingthosecriticalareasanddesignatingimprovementeffortsasSixSigmaBlackBeltprojects.Selectingtoppeopletoworkontheprojects--fulltime.Ensuringthesepeoplehavethetime,tools,andresourcestheyneedtosucceed.•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,价格,和貨期的意義.•品質,成本,准時走貨無不依耐于工序能力.WhatpurposeisSix-sigma?6σ推行教材BPTLConfidential18SixSigmaVisionTheVisionofSixSigmaistodelightcustomersbydeliveringworld-classqualityproductsthroughtheachievementofSixSigmalevelsofperformanceineverythingwedo.WhatpurposeisSix-sigma?SixSigmaPhilosophyThephilosophyofSixSigmaistoapplyastructured,systematicapproachtoachievebreakthroughimprovementacrossallareasofourbusiness.6σ推行教材BPTLConfidential192308,537366,80746,210523363.4sPPMProcessCapabilityDefectsperMillionOpp.SixSigma-AggressiveGoalWhatpurposeisSix-sigma?6σ推行教材BPTLConfidential20StatisticalDefinitionofn-SigmaLSLLSLUSLUSLProcessWidthmoDesignWidthTTscaleLSLLSLUSLUSLscaleTT+nsscale-nsThisistheso-calledn-sigmaSigmaisastatisticalunitofmeasurethatreflectsprocesscapability.Thesigmascaleofmeasureisperfectlycorrelatedtosuchcharacteristicsasdefects-per-unit,parts-permilliondefective,andtheprobabilityofafailure/error.σ推行教材BPTLConfidential223Sigma6Sigma5Sigma4Sigma93.32%99.379%99.9767%99.99966%HistoricalCurrentIntermediateLong-RunSigmaLong-TermYieldStandard6σ-PerformanceTargetCharacterizeOptimizeBreakthroughUSLTLSLUSLTLSLTUSLLSLUSL’LSL’TheStrategy6σ推行教材BPTLConfidential2