5StatisticalProcessControl

StatisticalProcessControlEngineering401-TotalQualityManagement1PatHammett1StatisticalProcessControlConcepts2HistoricalBackgroundnWalterShewhart(BellLaboratories-1920s).nsuggestedthateveryprocessexhibitssomedegreeofvariationandthereforeisexpected.nidentifiedtwotypesofvariation(chancecause)and(assignablecause).nproposedfirstcontrolcharttoseparatethesetwotypesofvariation.StatisticalProcessControlEngineering401-TotalQualityManagement2PatHammett3ProcessControl&SixSigmanMeasurementPhasenControlchartshelpidentifyifspecialcausesofvariationarepresent(σtotalσinherent).nUsedtoestimateprocessparameters(mean,standarddeviation,fractionnon-conforming)(randomvariation)(specialcauses-thesemaybe0)s2batchσ2productσ2gageσ2materialσ2inherentσ2processσ2total…4ProcessControlMethodsnStatisticalProcessControlnVariableControlChartsnX-bar/RangeChartnIndividual/MovingRangenAttributeControlChartsnP-charts-%non-conformingproductnOfcourse,otherprocesscontrolmethodsnAutomaticInspection(e.g.,poke-yoke)nAcceptanceSampling(notcoveredinclass)StatisticalProcessControlEngineering401-TotalQualityManagement3PatHammett5TheGenericControlChartSubgroup(intimesequence)QualityMeasureCenterLine(centraltendency)UpperControlLimitLowerControlLimit6KeyControlChartIssues1.IdentifyingVariableorstatistictotrack2.Defining“out-control”3.SampleSizeandFrequencyStatisticalProcessControlEngineering401-TotalQualityManagement4PatHammett71.VariableSelectionnSomechoicesofvariabletoPlotnVariable,SomeExamples:nIndividualvalue,XnX-barnRangesnAttributes,Someexamples:nFractionnon-conforming(p-charts)n#ofnon-conformities(e.g.,c-chart)nNote:mostunsuccessfulapplicationsofstatisticalprocesscontrol(SPC)chartsoccurbecausethewrongvariablesaremonitored.82.DefiningStatisticalControlnTypically,aprocessisdeemedin-controlifallsubgroupsfallwithin+/-3σcontrollimitsandnonon-randompatternsofbehaviorexist.nWhatisalphafor3σchartsifthedistributionofthecontrolcharacteristic(e.g.X-bar)isassumednormal?(Hint:whatisprobabilitythatyousayaprocessisout-control,whenitisnot.)nWhatareexamplesofnon-randompatterns?StatisticalProcessControlEngineering401-TotalQualityManagement5PatHammett9Examples:Non-randomPatternsnOneormorepointsplotsoutsidethecontrollimits.nArunof6consecutivepointsincreasingordecreasing.n9consecutivepointsaboveorbelowthecenterline.UCL=-.3122Average=-.5813LCL=-.8503.12-.23-.58-.93-1.29subgroup#13579111315171921232527293133Mean103.SampleSizeandFrequencynGeneralComments:nlargesamplesizesmakeiteasiertodetectsmallshifts,however,largesamplesaregenerallynon-economical.nMostapplicationsinvolvesmaller,morefrequentsamples,particularlyinhigh-volumemanufacturing,example:measure5partseveryhour.nMorerecenttrendtosmallsamplesizesoverlongerintervalsonceprocessesarebroughtintostatisticalcontrol(especially,ifthepartspermilliondefectsislow).nGoal:identifyRationalSamplingandSubgroupingStatisticalProcessControlEngineering401-TotalQualityManagement6PatHammett11RationalSampling&SubgroupsRationalSamplingnFrequentenoughtodetectimportantchangesthatrelatetocustomerdissatisfaction.RationalSubgroupingnSamplesarerelativelyhomogenouswithinthesubgroup(example:5consecutiveparts).nNote:choiceofsubgroupscandramaticallychangeestimateofwithinsubgroupvariationandthuswhatisconsidered“out-control”.12UsingControlChartsnTomonitoraprocess,wetypicallyusetwocontrolcharts.1)Monitorwithinsubgroupvariation(suchassubgrouprangeorstandarddeviation).2)Monitorbetweensubgroupvariation(suchasthemeanormedian)StatisticalProcessControlEngineering401-TotalQualityManagement7PatHammett13BasicStepstoApplySPC1.Identifyprocesscharacteristictostudy(e.g.,partlength).§Typicallychoosecharacteristicsthatarecreatingqualityproblemsorarecriticaltocustomer.2.Determineasamplingmethodandplan.nidentifyrationalsubgroups(e.g.,5consecutiveparts)nchoosesubgroupsize(typically3-5samplespersubgroup)ngenerally,collect20-25subgroups(100totalsamples)beforecalculatinginitialcontrollimits.nestablishsamplingfrequency(shouldbeasfrequentasneededtodetectunacceptablepatternsinthedata)14BasicStepstoApplySPC3.Datacollection-runtheprocessuntouchedtogatherinitialdataforcontrollimits.4.Establishcontrollimitstodetect“unstable”conditionsn“control”isuser-definedbuttypicallyuse+/-3σlimits.5.Plotoutputcharacteristiconcontrolchart6.Ifallpointsarein-control--stableprocessnifinitialpoint(s)areout-of-control,trytoidentifycauseandthenre-computelimitsaftereliminatingout-of-controlpoints.StatisticalProcessControlEngineering401-TotalQualityManagement8PatHammettSPCDatafromaStampedPart(subgroupsize=5)Subgroup(i)obs1obs2obs3obs4obs5Range(i)Xbar(i)10.14-0.170.14-0.200.080.340.002-0.20-0.160.16-0.160.400.500.013-0.080.24-0.240.040.080.480.014-0.20-0.16-0.24-0.28-0.200.12-0.225-0.20-0.16-0.360.04-0.120.40-0.166-0.280.280.20-0.040.120.560.067-0.12-0.160.280.200.160.440.0780.400.12-0.200.000.120.600.099-0.08-0.08-0.36-0.20-0.160.28-0.18100.160.32-0.120.16-0.240.560.0611-0.200.000.000.000.160.36-0.01120.040.000.00-0.12-0.080.16-0.0313-0.080.120.16-0.200.240.440.0514-0.16-0.040.12-0.20-0.080.32-0.0715-0.0