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Dec18,2001BPTLConfidential1Six-SigmaTrainingBookSix-SigmaTrainingBookBPTLConfidential26σ推行教材數据分布BPTLConfidential36σ推行教材NormalExponentialWeibullLognormaltc2fContinuousDistributionsSamplingDistributions數据分布BPTLConfidential46σ推行教材Themostwidelyusedmodelforthedistributionofcontinuousrandomvariable.Arisesinthestudyofnumerousphysicalphenomena,suchasthevelocityofmolecules.正態分布xe21xf2x21σμπσPlotisknownasProbabilityDensityFunctionofXBPTLConfidential56σ推行教材Manynaturalphenomenaandman-madeprocessesareobservedtohavenormaldistributions,orcanbecloselyrepresentedasnormallydistributed.Forexample,thelengthofamachinedpartisobservedtovaryaboutitsmeandueto:temperaturedrift,humiditychange,vibrations,cuttinganglevariations,cuttingtoolwear,bearingwear,rotationalspeedvariations,fixturingvariations,rawmaterialchangesandcontaminationlevelchangesIfthesesourcesofvariationaresmall,independentandequallylikelytobepositiveornegative,thelengthwillcloselyapproximateanormaldistribution.正態分布BPTLConfidential66σ推行教材FirstintroducedbyFrenchmathematicianAbrahamDeMoivrein1733.Madefamousin1809byGermanmathematicianK.F.Gausswhenhealsodevelopedanormaldistributionindependentlyanduseditinhisstudyofastronomy.Asaresult,itisalsoknownastheGaussiandistribution.Duringmidtolatenineteenthcentury,manystatisticiansbelievedthatitwas“normal”formostwell-behaveddatatofollowthiscurve.正態分布-歷程表KarlFriedrichGaussBPTLConfidential76σ推行教材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BPTLConfidential86σ推行教材Anormaldistributioncanbecompletelydescribedbyknowingonlythe:Mean()Variance()正態分布的一些特性DistributionOneDistributionOneDistributionTwoDistributionTwoDistributionThreeDistributionThreeWhatisthedifferencebetweenthe3normaldistributions?xe21xf2x21σμπσX~N(m,s2)1BPTLConfidential96σ推行教材A~Normal(A,A²)B~Normal(B,B²)A~Normal(A,A²)B~Normal(B,B²)A~Normal(A,A²)B~Normal(B,B²)WhatisthedifferencebetweenprocessA&Bforeachcase?正態分布的一些特性BPTLConfidential106σ推行教材Themean,medianandmodeallcoincideatthesamevalue-.Thereisperfectsymmetry.µµ+-MeanMedianMode2Themeanrepresentsthearithmeticaverageofallobservationsinadataset.Ifasetofobservationsisarrangedinanincreasingorderofmagnitude(rankeddata),themiddlevalueiscalledthemedian.Ifthenumberofobservationsisodd,themedianisthevalueofthemiddlenumber.Ifthenumberofobservationsiseven,thereare2middlenumbers,andthemedianistheaverageofthe2values.Themodeistheobservationthatoccursmostfrequentlyinthesample.正態分布的一些特性BPTLConfidential116σ推行教材Theareaundersectionsofthecurvecanbeusedtoestimatethecumulativeprobabilityofacertain“event”occurring:µµPointofInflection1s1s+¥-¥68.27%95.45%99.73%m+/-3sisoftenreferredtoasthewidthofanormaldistribution3正態分布的一些特性BPTLConfidential126σ推行教材Let’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BPTLConfidential136σ推行教材MiniTab:CalcProbabilityDistributionsNormal...Entermv...