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1、Six-SigmaTrainingBookSix-SigmaDec18,20011BPTLConfidential數据分布2BPTLConfidentialNormalExponentialWeibullLognormaltc2fContinuousDistributionsSamplingDistributions數据分布3BPTLConfidentialThemostwidelyusedmodelforthedistributionofcontinuousrandomvariable.Arisesinthes
2、tudyofnumerousphysicalphenomena,suchasthevelocityofmolecules.正態分布PlotisknownasProbabilityDensityFunctionofX4BPTLConfidentialManynaturalphenomenaandman-madeprocessesareobservedtohavenormaldistributions,orcanbecloselyrepresentedasnormallydistributed.Forexample,
3、thelengthofamachinedpartisobservedtovaryaboutitsmeandueto:temperaturedrift,humiditychange,vibrations,cuttinganglevariations,cuttingtoolwear,bearingwear,rotationalspeedvariations,fixturingvariations,rawmaterialchangesandcontaminationlevelchangesIfthesesourceso
4、fvariationaresmall,independentandequallylikelytobepositiveornegative,thelengthwillcloselyapproximateanormaldistribution.正態分布5BPTLConfidentialFirstintroducedbyFrenchmathematicianAbrahamDeMoivrein1733.Madefamousin1809byGermanmathematicianK.F.Gausswhenhealsodeve
5、lopedanormaldistributionindependentlyanduseditinhisstudyofastronomy.Asaresult,itisalsoknownastheGaussiandistribution.Duringmidtolatenineteenthcentury,manystatisticiansbelievedthatitwas“normal”formostwell-behaveddatatofollowthiscurve.正態分布-歷程表KarlFriedrichGauss
6、6BPTLConfidential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7BPTLConfidentialAnormaldistributioncanbecompletelydescribedbyknowingonlythe:Mean(m)Variance(s2)正態分布的一些特性DistributionOneDistributi
7、onTwoDistributionThreeWhatisthedifferencebetweenthe3normaldistributions?X~N(m,s2)18BPTLConfidentialA~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9BPTLCo
8、nfidentialThemean,medianandmodeallcoincideatthesamevalue-m.Thereisperfectsymmetry.µ+¥-¥MeanMedianMode2Themeanrepresentsthearithmeticaverageofallobservationsinadataset.Ifasetofobservations
