09Capability(制程能力)

TRAININGCONSULTINGSixSigmaTrainingSOFTWAREProcessCapabilityandTheStandardTransformChampionTrainingUSLImproveAnalyzeMeasureControlSixSigmaTraining2AssessingProcessCapabilityforVariableData•VerifySpecificationandMeasurementSystem•Takeashorttermorlongtermsample•VerifyProcessStability•CalculateCp,Cpk,Pp,Ppk,DPUandPPM•CalculateZ-scoreshorttermandlongterm(SigmaLevel)VerifySpec`sTakeSampleVerifyProcessStabilityCalculateCp,Cpk,Pp,Ppk,DPU&PPMCalculateZ-stZ-ltSixSigmaTraining3GeneralForm:Z=(x-x)ThistransformproducesavaluefromadistributionwheretheMean=0and=1.Thevalueindicateshowfarthenumberisfromthemeaninunitsofstandarddeviations.Forexample,ifZ=2,thatwouldsaythatthenumberinquestionis2standarddeviationsawayfromtheMean.Forestimatingouryieldforaprocess,wewillsubstitutetheLowerSpecLimit(LSL)andtheUpperSpecLimit(USL)forx.Byusingthismethod,wecancalculatetheproportionofproductthatisout-of-specbasedonthatproductsOutputMeanand.Let’slookatanexample.TheStandardTransformSixSigmaTraining4Z-TransformExampleMean=1.03LSL=0.90=0.0573USL=1.101.31.21.11.00.90.87006005004003002001000rawFrequencyUSLLSLSixSigmaTraining5Z-TransformThetaskistodetermineestimatesoftheproportionofthenormalcurvethatisoutsidetheupperandlowerspecificationlimits.WedothatbycalculatingZ-scoreforeachspeclimit.Z=(LSL-x)=0.9-1.03.0573=-2.27LZ=(USL-x)=1.1-1.03.0573=1.22UWecannowcalculatetheareasbelowthelowerspecandabovetheupperspecusingthenormalprobabilityfunction.SixSigmaTraining6ExampleStandardScoreDistributionRawScoreDistribution1.31.21.11.00.90.87006005004003002001000rawFrequencyUSLLSL43210-1-2-3-45004003002001000C2FrequencyLSLUSLSixSigmaTraining7ExampleTheFractionOutsidetheSpecLimitscanbedeterminedbyusingNormalTableorMinitabFunctions.Pr(x0.9)+Pr(x1.1)=Pr(Z-2)+Pr(Z1)=1.16%+11.12%12%..2722Wheredowegettheprobabilities?TheNormalTableorMinitab.CalcProbabilityDistributionNormalCumulativeProbability.SixSigmaTraining8RelatingZ-ScorestoSixSigmaToAchieveSixSigma,theZ-scoresfortheUSLandLSLshouldbeatleast6.00eachinashort-termcapabilityStudy.Thatsaysthatthemeanofthedistributionissixstandarddeviationsawayfromthespeclimit.TocalculatetheZ-scorefortheprocess,wemustusethefollowingprocedure:1.AddthepercentagescalculatedtobeoutsidetheUSLandLSL.2.UsethetableoftheNormalCurveorMinitab’sInverseCumulativeDistributionFunctiontoconvertthepercentageoutsidespecificationtoaZ-score3.Ifwehaveshort-termprocessdata,thisZ-scoredirectlyrepresentsourshortterm-sigmalevel.Toestimatethelong-termsigmalevel,wesubtract1.5.4.Ifwehavelong-termprocessdata,weadd1.5totheabsolutevalueofthatZ-scoretodetermineourshorttermsigmalevel.SixSigmaTraining9ShortandLongTermProcessData•ShortTermprocessdatacoversarelativelyshortperiodoftime(lessthanoneshift/day)consistingof30to50datapointsthatincludeonlycommoncauses.•LongTermprocessdatacoversarelativelylongperiodoftime(Weeks,Months)consistingof200ormoredatapointsthatincludedifferentoperators,manyshifts,differentpiecesofequipmentetc.2001000543ObservationNumberIndividualValueLongTermprocessdataforBuckleRelease1X=3.7403.0SL=4.596-3.0SL=2.884504030201004.53.52.5ObservationNumberIndividualValueShortTermProcessDataforBuckleReleaseX=3.6553.0SL=4.588-3.0SL=2.723SixSigmaTraining10TheZ-Transform&ST/LTDataST(Short-Term)LT(Long-Term)STLT=T(Target)(Mean)SL=USLLSLZSL-.KnowwhetheryourdataisShortTermorLongTermSixSigmaTraining11AStatisticalLookatST<Data•Comparetheestimatesoftheprocessst.dev.’sfromtheShortTermandLongTermdata.•Open‘Bklrelea.mtw’andchoose:•StatBasicStatisticsDescriptiveStatisticsDescriptiveStatisticsVariableNMeanMedianTrMeanStDevSEMeanLongtRel2003.74033.76503.73490.37710.0267ShortRel503.65523.68003.65390.33730.0477VariableMinMaxQ1Q3LongtRel2.98004.65003.42003.9800ShortRel2.98004.25003.29753.9050WhatisthedifferencebetweentheShortTermandtheLongTermSt.Dev.?SixSigmaTraining12TheIdeaofRationalSubgroups•Goal:Toestablishasamplingwindowsmallenoughtoexcludesystematicnonrandominfluences.•IntendedResult:Dataexhibitingonlycommoncausevariationwithingroupsofnitemsandspecialcause(ifitexists)variationbetweengroups.•Ifdonecorrectly,averaged(Pooled)sigma’sfromthesubgroupsgiveusagoodestimateofourbestcaseprocesscapabilitybasedonthecurrentprocess.•Ifthereisabigdifferencebetweenthepooledstandarddeviationandthestandarddeviationbasedonthetotaldataset,wehaveshiftsintheprocessmeanorsigmaovertime.SixSigmaTraining13AnExampleofRationalSubgroups76543210232221201918171615141312111098765432103.52.51.5HourOutputHowdoesthe‘WithinGroups’sigmarelatetotheTotalsigma?Hint:YoucanruntheDescriptiveStatprocedureforthetotaldatasetandthenrunitagainusingtheBYvariableoptionwithShiftasthevariable.Openthefile‘Ratsubgr’mtw.PlotthedatausingtheTimeSeriesplot.Usethe‘Reference’optionunderFrameforgraphingshiftboundarylines.DemonstrationofRationalSubgroupsShiftistheGroupingVariableSixSigmaTraining14DescriptiveStatistics(StatBasicStatisticsDescriptiveStatistics)VariableNMeanMedianTrMeanStDevSEMeanOutput322.3762.3272.3760.7980.141NowrunDescriptiveStatisticsusingthe‘ByVariable’function:StatBasicStatistics