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

Dec18,2001,BPTLConfidential,1,Six-SigmaTrainingBook,Six-Sigma,BPTLConfidential,2,數据分布,BPTLConfidential,3,NormalExponentialWeibullLognormaltc2f,ContinuousDistributions,SamplingDistributions,數据分布,BPTLConfidential,4,Themostwidelyusedmodelforthedistributionofcontinuousrandomvariable.Arisesinthestudyofnumerousphysicalphenomena,suchasthevelocityofmolecules.,正態分布,PlotisknownasProbabilityDensityFunctionofX,BPTLConfidential,5,Manynaturalphenomenaandman-madeprocessesareobservedtohavenormaldistributions,orcanbecloselyrepresentedasnormallydistributed.Forexample,thelengthofamachinedpartisobservedtovaryaboutitsmeandueto:temperaturedrift,humiditychange,vibrations,cuttinganglevariations,cuttingtoolwear,bearingwear,rotationalspeedvariations,fixturingvariations,rawmaterialchangesandcontaminationlevelchangesIfthesesourcesofvariationaresmall,independentandequallylikelytobepositiveornegative,thelengthwillcloselyapproximateanormaldistribution.,正態分布,BPTLConfidential,6,FirstintroducedbyFrenchmathematicianAbrahamDeMoivrein1733.Madefamousin1809byGermanmathematicianK.F.Gausswhenhealsodevelopedanormaldistributionindependentlyanduseditinhisstudyofastronomy.Asaresult,itisalsoknownastheGaussiandistribution.Duringmidtolatenineteenthcentury,manystatisticiansbelievedthatitwas“normal”formostwell-behaveddatatofollowthiscurve.,正態分布-歷程表,KarlFriedrichGauss,BPTLConfidential,7,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,BPTLConfidential,8,Anormaldistributioncanbecompletelydescribedbyknowingonlythe:Mean(m)Variance(s2),正態分布的一些特性,Whatisthedifferencebetweenthe3normaldistributions?,XN(m,s2),1,BPTLConfidential,9,WhatisthedifferencebetweenprocessA&Bforeachcase?,正態分布的一些特性,BPTLConfidential,10,Themean,medianandmodeallcoincideatthesamevalue-m.Thereisperfectsymmetry.,MeanMedianMode,2,Themeanrepresentsthearithmeticaverageofallobservationsinadataset.,Ifasetofobservationsisarrangedinanincreasingorderofmagnitude(rankeddata),themiddlevalueiscalledthemedian.Ifthenumberofobservationsisodd,themedianisthevalueofthemiddlenumber.Ifthenumberofobservationsiseven,thereare2middlenumbers,andthemedianistheaverageofthe2values.,Themodeistheobservationthatoccursmostfrequentlyinthesample.,正態分布的一些特性,BPTLConfidential,11,Theareaundersectionsofthecurvecanbeusedtoestimatethecumulativeprobabilityofacertain“event”occurring:,PointofInflection,1s,+,-,68.27%,95.45%,99.73%,m+/-3sisoftenreferredtoasthewidthofanormaldistribution,3,正態分布的一些特性,BPTLConfidential,12,Letscomputethecumulativeprobabilitiesofthefollowingdistributions:,m=3.5s=0.6,1.8,20.0,m=16.6s=2.8,m=-1.5s=0.9,-2.8,0.5,正態分布的一些特性,BPTLConfidential,13,MiniTab:CalcProbabilityDistributionsNormal.,Entermvalue,Entersvalue,Enterxvalue,正態分布的一些特性,BPTLConfidential,14,什么是6,?,?,?,BPTLConfidential,15,6簡介,BPTLConfidential,16,TheFocusofSixSigma,Identifyingcriticalaspectsofthebusinesswithproblemsoropportunitiesforimprovement.TargetingthosecriticalareasanddesignatingimprovementeffortsasSixSigmaBlackBeltprojects.Selectingtoppeopletoworkontheprojects-fulltime.Ensuringthesepeoplehavethetime,tools,andresourcestheyneedtosucceed.,BPTLConfidential,17,CustomerFocus:AModelForSuccess,Technology,Technology,Capability,Capability,Organization,Organization,People,People,Processes,Processes,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?,BPTLConfidential,18,SixSigmaVision,TheVisionofSixSigmaistodelightcustomersbydeliveringworld-classqualityproductsthroughtheachievementofSixSigmalevelsofperformanceineverythingwedo.,WhatpurposeisSix-sigma?,SixSigmaPhilosophy,ThephilosophyofSixSigmaistoapplyastructured,systematicapproachtoachievebreakthroughimprovementacrossallareasofourbusiness.,BPTLConfidential,19,PPM,ProcessCapability,DefectsperMillionOpp.,SixSigma-AggressiveGoal,WhatpurposeisSix-sigma?,BPTLConfidential,20,StatisticalDefinitionofn-Sigma,LSL,LSL,USL,USL,ProcessWidth,m,o,DesignWidth,T,T,scale,LSL,LSL,USL,USL,scale,T,T,+n,s,scale,-n,s,Thisistheso-calledn-sigma,Sigmaisastatisticalunitofmeasurethatreflectsprocesscapability.Thesigmascaleofmeasureisperfectlycorrelatedtosuchcharacteristicsasdefects-per-unit,parts-permilliondefective,andtheprobabilityofafailure/error.,BPTLConfidential,21,StatisticalDefinitionof6,Thisisthesix-sigmawesaid,LSL,LSL,USL,USL,ProcessWidth,m,o,DesignWidth,+3,s,st,T,T,.001,ppm,USL,.001,ppm,2)b)工序能力可(Cp=1to2)c)工序能力差(Cp1.5)b)工序能力可(Cpk=1to1.5)c)工序能力差(Cpk1),BPTLConfidential,44,工序潛力与工序表現,(a)PoorProcessPotential(b)PoorProcessPerformance,ExperimentalDesigntoreducevariation,ExperimentalDesigntocentermeantoreducevariation,BPTLConfidential,45,工序潛力与工序表現,BPTLConfidential,46,工序穩定性,Aprocessisstableifthedistributionofmeasurementsmadeonthegivenfeatureisconsistentovertime.,Time,StableProcess,Time,UnstableProcess,BPTLConfidential,47,短期工序能力与長期工序能力,短期工序能力(previouslycalledshort-termcapability)showstheinherentvariabilityofamachine/processoperatingwithinabriefperiodoftime.長期工序能力(previouslycalledlong-termcapability)showsthevariabilityofamachine/processoperatingoveraperiodoftime.Itincludessourcesofvariationinadditiontotheshort-termvariability.,BPTLConfidential,48,WithinOverallSampleSize3050units100unitsNumberofLotssinglelotseverallotsPeriodofTimehoursordaysweeksormonthsNumberofOperatorssingleoperatordifferentoperatorsProcessPotentialCpPpProcessPerformanceCpkPpk,短期工序能力与長期工序能力,BPTLConfidential,49,實戰演練,Thelengthofacamshaftforanautomobileengineisspecifiedat6002mm.Controlofthelengthofthecamshaftiscriticaltoavoidscrap/rework.Thecamshaftisprovidedbyexternalsuppliers.Assesstheprocesscapabilityforthissupplier.ThedataisavailableinCamshaft.MTW.Dataarecollectedinsubgroupsof5each.,BPTLConfidential,50,Example4,Minitab:StatQualityToolsCapabilityAnalysis(Normal),BPTLConfidential,51,Example4,BPTLConfidential,52,Example5,Histogramofthecamshaftlengthsuggestsmixedpopulations.Furtherinvestigationrevealedthattherearetwosuppliersforthecamshaft.Datawerenowcollectedoncamshaftsfromeachsourcewithoutcombiningboth.Subgroupsizeis5foreachsupplier.Arethetwosupplierssimilarinperformance?Ifnot,whatareyourrecommendations?,BPTLConfidential,53,Example5,MiniTab:StatQualityToolsCapabilitySixpack(Normal),BPTLConfidential,54,Example5,BPTLConfidential,55,Example5,BPTLConfidential,56,用Box-Cox轉化后的工序能力分析,Whentheprocessdataarenotnormal,theCpkorPpkindicesarenotaccurateorreliable,becausetheseindicesarecomputedonthebasisthatthedataarenormallydistributed.Dppmvaluesassociatedwiththeindiceswillnotbeneartotheactualperformancewhenthenormalcurvedoesnotmodeltheactualdatawell.,BPTLConfidential,57,Iftheprocessdataaresomewhatbell-shapedbutskewed,Box-Coxtransformationcanbeusedtomakethedatanormalbeforeweassesstheprocesscapability.RemembertotransformthespecificationlimitstoobeforewecomputeCpkorPpk!,用Box-Cox轉化后的工序能力分析,BPTLConfidential,58,Minitab:StatQualityToolsCapabilityAnalysis(Normal),用Box-Cox轉化后的工序能力分析,BPTLConfidential,59,Example6,OpenthefilenamedDimension.MTWintheDay-2folderagain.Computetheprocesscapabilitywiththespecificationlimits:LSL:0.1USL:10Arethedatanormallydistributed?ComputetheprocesscapabilityagainwithBox-Coxtransformation.,用Box-Cox轉化后的工序能力分析,BPTLConfidential,60,Cpkof0.41isreportedintheSSATpackage.Thisvalueisnotreliableoraccurateifthedataarenotnormal.,Dataisnotnormal,Example6,用Box-Cox轉化后的工序能力分析,BPTLConfidential,61,Example6,Cpkhasincreasedfrom0.41to0.81,用Box-Cox轉化后的工序能力分析,BPTLConfidential,62,Whats“6”QualityThen,OriginalDefinitionbyMotorola:Intheshortterm,thespecificationlimitsareatleast6awayfromtheprocessmean,i.e.Cp2,Inthelongrun,theprocesswillshiftbylessthan1.5,i.e.Ppk1.5,Theprocesswillyieldlessthan3.4dppmrejectedparts.,Shift1.5,“SigmaLevel”Capability,BPTLConfidential,63,WhatsSixSigmaQualityNow,MikelJHarryclaimsthattheprocessmeanbetweenl