09Capability.ppt

ProcessCapabilityandTheStandardTransform ChampionTraining USL Improve Analyze Measure Control AssessingProcessCapabilityforVariableData VerifySpecificationandMeasurementSystemTakeashorttermorlongtermsampleVerifyProcessStabilityCalculateCp Cpk Pp Ppk DPUandPPMCalculateZ scoreshorttermandlongterm SigmaLevel GeneralForm ThistransformproducesavaluefromadistributionwheretheMean 0and 1 Thevalueindicateshowfarthenumberisfromthemeaninunitsofstandarddeviations Forexample ifZ 2 thatwouldsaythatthenumberinquestionis2standarddeviationsawayfromtheMean Forestimatingouryieldforaprocess wewillsubstitutetheLowerSpecLimit LSL andtheUpperSpecLimit USL forx Byusingthismethod wecancalculatetheproportionofproductthatisout of specbasedonthatproductsOutputMeanand Let slookatanexample TheStandardTransform Z TransformExample Mean 1 03LSL 0 90 0 0573USL 1 10 Z Transform Thetaskistodetermineestimatesoftheproportionofthenormalcurvethatisoutsidetheupperandlowerspecificationlimits WedothatbycalculatingZ scoreforeachspeclimit Wecannowcalculatetheareasbelowthelowerspecandabovetheupperspecusingthenormalprobabilityfunction Example StandardScoreDistribution RawScoreDistribution Example TheFractionOutsidetheSpecLimitscanbedeterminedbyusingNormalTableorMinitabFunctions Wheredowegettheprobabilities TheNormalTableorMinitab Calc ProbabilityDistribution Normal CumulativeProbability RelatingZ ScorestoSixSigma ToAchieveSixSigma 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 ShortandLongTermProcessData ShortTermprocessdatacoversarelativelyshortperiodoftime lessthanoneshift day consistingof30to50datapointsthatincludeonlycommoncauses LongTermprocessdatacoversarelativelylongperiodoftime Weeks Months consistingof200ormoredatapointsthatincludedifferentoperators manyshifts differentpiecesofequipmentetc TheZ Transform ST LTData ST Short Term LT Long Term KnowwhetheryourdataisShortTermorLongTerm AStatisticalLookatST LTData Comparetheestimatesoftheprocessst dev sfromtheShortTermandLongTermdata Open Bklrelea mtw andchoose Stat BasicStatistics DescriptiveStatisticsDescriptiveStatisticsVariableNMeanMedianTrMeanStDevSEMeanLongtRel2003 74033 76503 73490 37710 0267ShortRel503 65523 68003 65390 33730 0477VariableMinMaxQ1Q3LongtRel2 98004 65003 42003 9800ShortRel2 98004 25003 29753 9050 WhatisthedifferencebetweentheShortTermandtheLongTermSt Dev TheIdeaofRationalSubgroups Goal Toestablishasamplingwindowsmallenoughtoexcludesystematicnonrandominfluences IntendedResult Dataexhibitingonlycommoncausevariationwithingroupsofnitemsandspecialcause ifitexists variationbetweengroups Ifdonecorrectly averaged Pooled sigma sfromthesubgroupsgiveusagoodestimateofourbestcaseprocesscapabilitybasedonthecurrentprocess Ifthereisabigdifferencebetweenthepooledstandarddeviationandthestandarddeviationbasedonthetotaldataset wehaveshiftsintheprocessmeanorsigmaovertime AnExampleofRationalSubgroups Howdoesthe WithinGroups sigmarelatetotheTotalsigma Hint YoucanruntheDescriptiveStatprocedureforthetotaldatasetandthenrunitagainusingtheBYvariableoptionwithShiftasthevariable Openthefile Ratsubgr mtw PlotthedatausingtheTimeSeriesplot Usethe Reference optionunderFrameforgraphingshiftboundarylines DemonstrationofRationalSubgroupsShiftistheGroupingVariable DescriptiveStatistics Stat BasicStatistics DescriptiveStatistics VariableNMeanMedianTrMeanStDevSEMeanOutput322 3762 3272 3760 7980 141NowrunDescriptiveStatisticsusingthe ByVariable function Stat BasicStatistics DescriptiveStatistics Variables Output Byvariable Shift DescriptiveStatisticsVariableShiftNMeanMedianTrMeanStDevSEMeanOutput181 60261 61771 60260 18170 0642283 10203 11293 10200 20470 0724381 61501 62841 61500 15830 0560483 18313 23313 18310 17080 0604 ResultsofDescriptiveStatistics Whatimplicationdoesthishaveinstudyingprocesscapability Whatsigmarepresentstherealprocesscapability Whatsigmarepresentsthepotentialprocesscapability ComponentsofVariationandRationalSubgroups TotalSumofSquares BetweenGrpSS WithinGrpSS TotalVariability MeanShiftVariability PooledWithinGrpsVariability ComponentsofVariationandRationalSubgroups Capability Precision Accuracy TotalSumofSquares BetweenGrpSS WithinGrpSS VisualizingtheProcessDynamics Overtime a typical processwillshiftanddriftbyapprox 1 5 ShortTermCapability LSL USL T Time1 Time2 Time3 Time4 Pooledstd dev Overallstd dev WITHINGROUP BETWEENGROUP VisualizingtheComponentsofVariability USL LSL Theeffectofprocessshiftovertimeis1 5sigma 3SigmaProcessNoMeanShift 3SigmaProcessMeanShiftof1 5sigma SixSigmaProcessNoMeanShift SixSigmaProcessMeanShiftof1 5sigma ShortTermProcessCapabilityRatios st CpassumestheProcessisCentered ShortTermProcessCapabilityRatios CpkaccountsfortheMeanShiftintheProcess st st LongTermProcessCapabilityRatios ProcessWidth 3 3 T LSL USL PpassumestheProcessisCentered NormalVariationoftheProcess LongTermProcessCapabilityRatios PpkaccountsfortheMeanShiftintheProcess Ppk Pp 1 k where T X3 K lt TheProcessImprovementPlancallsforperformingaShort termCapabilitystudyduringtheMeasurementPhasetoestablishtheprocessbaseline Minitab sprocesscapabilityfunctionsallowyouoptionsonwhatstd dev touseinthecapabilityratiocalculations Short termCapabilityusesthewithinsubgroupstandarddeviationcalculatedinMinitab Thismeasuresthe instantaneous capabilityandmaybeusedtoestablishprocessentitlement Long termcapabilityusestheOverallStandardDeviation Total Byusingtheoverallstandarddeviation yougetthebestestimateofyourlongtermcapability ProcessImprovementPlan AssessingProcessCapabilityforAttributeData VerifyAttributeMeasurementSystemCountprocessdefectsandtotalunitsprocessedCalculatePPMandDPU Defectsperunit CalculateZ scoreshorttermandlongterm SigmaLevel AssessingProcessCapabilityforAttributeData CalculateDPU PPMandZ scoreforthefollowingprocess Totaldefects 976Totalunitsproduced 9 000DPU 0 108444PPM 108 444Zlt 1 23Zst 1 23 1 50 2 73 WhatDoesAllThisMean Short Term C p toRTY C