工程能力(1)

ProcessCapability(工程能力)Sept.16,2003SEQContentsDefinitionObjectiveDesignforPCSPopulationandSampleHowtoperformaPCSHowtointerpretaPCSDefinitionMachineCapability:Variationcausedbythemachineandnotthevariationcausedbyotherpartsoftheprocess.ProcessCapability:Variationcausedbyallthesourcesofvariation-themachine,thematerialused,themethodsemployed,theoperators,involved,andtheenvironmentasitaffectstheproducts.DefinitionInclude:Changesinincomingshipmentsofmaterials,Shiftsintemperatures,Toolwear,Useofdifferentoperators,SmallchangesinmethodsWhenyouestimatetheprocesscapability,ObjectiveOldProcessesNewProcessesNewMaterialEvaluationProductSpecificationsProcessManagementProductDesignProblemSolvingUSES:DesignforPCSTerminology:SubgroupWindow⇒TimeBetweenSubgroups⇒Specimen⇒Sample⇒SampleSize⇒Thedurationofeach‘sampling’periodThedurationofeach‘nosampling’periodAnindividualunitofproductThecollectionofSpecimensgatheredduringasubgroupwindowThenumberofspecimensinthesampleDesignforPCSHowtotakesample:SamplingNoSamplingSamplingNoSamplingTime“NoSampling”intervalsshouldbeofvaryinglength-randomlyDesignforPCSStandardDeviations:Sigma(σ)isusedtorepresentstandarddeviationσs:Specimen–to-specimenstandarddeviationσw:Window–to-windowstandarddeviationσh:HistoricalstandarddeviationDesignforPCSProcessVariation:ThetotalamountofprocessVariation(σh)isacombinationofσsandσw.σh=√σ²s+σ²wPopulationandSamplePopulation(母集團)Sample(標本)RemarkSizeMean(平均)Variance(分散)StandardDeviation(標準扁差)Nμσ²σnxs²sE(X)=μE(S²)=σ²PopulationandSampleObjectivePopulationSampleDataActiononaproductionprocess:ProcesscontrolProcessanalysisActiononalot:InspectionEstimationofqualityProcessLotSampleLotSampleDataDataSamplingActionMeasurementSamplingActionMeasurementHowtoperformaPCS1.DefiningtheObjectiveofthePCS•Examinationofprocessstability•LookingforaCPKvalue•Estimationofthesteady-stateprocessvariation•MaintainingcontrolchartsafterthePCS•……?HowtoperformaPCS2.SettingOperatingConditions•Theconditionswillvaryfromstudytostudydependingontheobjectives.-Machineadjustments?-Operatingcrewschange?-Rawmaterialslotchange?-Linespeedchange?HowtoperformaPCS3.DesigningthePCS1)SubgroupwindowThedecisiononhowlargetomakethesubgroupwindowdependsontheobjectiveofthePCS.Ex)Iftheobjectiveistostudytheextremeshorttermvariationoftheprocess,thesubgroupwindowwouldbechosentobeassmallaspossible.ThespecimensgatheredduringeachsubgroupwindowmustbedrawnatrandomHowtoperformaPCS3.DesigningthePCS2)SampleSizeAlargesamplesizeprovidesmoresensitivityfordetectingshiftsinmeanandstandarddeviation.Samplesizedeterminationisastatisticalandeconomicissue.Reasonablesamplesize:4-5HowtoperformaPCS3.DesigningthePCS3)NumberofSubgroupsTheremustbeenoughsubgroupstoproperlyestimatethecontrolchartparameters.Minimumsubgroups:20ThenumberofsubgroupstogetherwiththesubgroupwindowdeterminesthelengthofthePCS.HowtoperformaPCS3.DesigningthePCS4)TimeBetweenSubgroupsThetimesbetweensubgroupsshouldbeofvaryinglengthtoavoidpossiblecoincidencewithaprocesscycle.T-WST=WS+(S-1)BB=S-1T:ThetotaldurationofthePCSW:ThesubgroupwindowS:ThenumberofsubgroupsB:ThetimebetweensubgroupsHowtoperformaPCSHowtoperformaPCS4.PerformingthePCS1)ThemeasurementofeachspecimenEachspecimengatheredduringthePCSismeasuredforaspecificsetofproperties.EachspecimenmustretainitsidentitythroughoutthePCS.SpecimensshouldbetestedinrandomorderVariationofrecalibration,differentinstrumentsand/ortechnicians…HowtoperformaPCS4.PerformingthePCS2)ProcessCapability=6σProcesscapabilityisameasurablepropertyoftheprocess.Theresultingmeasureisexpressedintermsof6σofvariation.σ=thestandarddeviationoftheprocessunderastateofstatisticalcontrol.Thestandarddeviationmeasuresthedistanceonthehorizontalscaleassociatedwiththe68.26%,95.46%,and99.7%.HowtoperformaPCSFigure:AreasunderthenormaldistributionX~N(μ,σ²)Xisnormallydistributedwithmeanμandvarianceσ²HowtoperformaPCS4.PerformingthePCS3)ProcessCapabilityMeasurement•Oneofmethodsformeasuringprocesscapabilityisthecontrolchartmethod.•X-Rcontrolchartsforvariablessuchaslengthorwidth,temperatureandvolume.•Theprocesscapabilityiscomputedas6σ,whichincludes99.73%ofthedata.HowtoperformaPCS4.PerformingthePCS4)StatisticalBasisoftheChartsIfx₁,x₂,…,xnisasampleofsizen,thentheaverageofthissampleisx₁+x₂+…+xnx=nTheprocessaverageisthegrandaveragex₁+x₂+…+xmx=mxwouldbeusedasthecenterlineonthexchartHowtoperformaPCSXisnormallydistributedwithmeanμandstandarddeviationσx=σ／√nSubgroupn=9n=4n=1μHowtoperformaPCS4.PerformingthePCS4)StatisticalBasisoftheChartsIfx₁,x₂,…,xnisasampleofsizen,thentherangeofthesampleisthedifferencebetweenthelargestandsmallestobservations;R=xmax–xminLetR₁,R₂,…,Rmbetherangeofthemsamples,R₁+R₂+…+RmR=mHowtoperformaPCS4.PerformingthePCS4)StatisticalBasisoftheChartsControlLimitsforthexchartUCL=x+A₂RCL=xLCL=x-A₂RTheconstantA₂istabulatedforvarioussamplesizesinTableVIHowtoperformaPCS4.PerformingthePCS4)StatisticalBasisoftheChartsControlLimitsfortheRchartUCL=D₄RCL=RLCL=D₃RTheconstantD₃andD₄aretabulatedforvariousvaluesofninTableVIHowtoperformaPCS4.PerformingtheP