ExampleofCapabilityAnalysisDataForsomecriticaldimensionsweneedtomeasuremorethan1partForcapabilitydataweusuallymeasure5pcs2times/hour=100pcs(butsamplingplanneedstobemadeonthebasisofproductionquantity,rundurationandcycletime)ProcessCapability-Whatisit?ProcessCapabilityisameasureoftheinherent

capabilityofamanufacturingprocesstobeabletoconsistentlyproducecomponentsthatmeettherequireddesignspecificationsProcessCapabilityisdesignatedbyCpandCpkProcessPerformanceisameasureoftheperformanceofaprocesstobeabletoconsistentlyproducecomponentsthatmeettherequireddesignspecifications.ProcessPerformanceincludesspecialcausesofvariationnotpresentinProcessCapabilityProcessPerformanceisdesignatedPpandPpkWhyMakeProcessCapabilityStudiesLSL(lowerspecificationlimit)10,7USL(upperspecificationlimit)10,9Nominal10,80,1Thispartiswithinspec.ThetoolwouldbeapprovedifonlythispartwasmeasuredThesepartsareoutofspecandcouldbeapprovedifonlyonegoodpartwasmeasuredAprocesscapabilitystudywouldrevealthatthetoolshouldnotbeacceptedWhenadimensionneedstobekeptproperlywithinspec,wemuststudytheprocesscapability….butstillthisisnoguaranteefortheactualperformanceoftheprocessasitisonlyaninitialcapabilitystudy

E1.5

E1

E2

E3

E4

E5TheNokiaProcessVerificationProcessBlackdiamondstobefixedbyE3(oftenachangeofawhitediamond)ProposalforblackdiamondstobediscussedwithSupplier.Max:105,85OngoingProcessControl(SPC)TolerancesappliedtodrawingType1FunctionalCharacteristics-1part/cavitymeasuredformeasurementreportWhitediamonds(s)tobeagreedWhitediamonds(s)tobediscussedwithsupplier10parts/cavitymeasuredformeasurementreportCapabilitystudy:Requirement:CpandCpk>1.67byE3.Quantitiestobeagreedwithsupplier.Minimum5partspr1/2hourin10hoursmeasuredforeachcavity=100parts.Canvarydependingontoolcapacity,e.g.stampedparts(seeDMY00019-EN)Section2.Population,SampleandNormalDistributionTheBellShaped(Normal)DistributionSymmetricalshapewithapeakinthemiddleoftherangeofthedata.Indicatesthattheinputvariables(X's)totheprocessarerandomlyinfluenced.“PopulationParameters”

=Populationmean

=PopulationstandarddeviationPopulationversusSamplePopulationAnentiregroupofobjectsthathavebeenmadeorwillbemadecontainingacharacteristicofinterestSampleThegroupofobjectsactuallymeasuredinastatisticalstudyAsampleisusuallyasubsetofthepopulationofinterestPopulationSample“SampleStatistics” x=Samplemean s=SamplestandarddeviationTheNormalDistributionWhatMeasurementsCanBeUsedtoDescribeaProcessorSystem?Example:1

=52

=73

=44

=25

=6mean(average)ordescribesthelocationofthedistributionμ(mü),ameasureofcentraltendency,isthemeanoraverageofallvaluesinthepopulation.Whenonlyasampleofthepopulationisbeingdescribed,meanismoreproperlydenotedas

(x-bar):Example:1

=52

=73

=44

=25

=6Themostsimplemeasureofvariabilityistherange.Therangeofasampleisdefinedbyasthedifferencebetweenthelargestandthesmallestobservationfromsamplesinasub-group,e.g.5consecutivepartsfromthemanufacturingprocess.WhatMeasurementsCanBeUsedtoDescribeProcessvariation?sST-oftennotatedas

orsigma,isanothermeasureofdispersionorvariabilityandstandsfor“short-termstandarddeviation”,whichmeasuresthevariabilityofaprocessorsystemusing“rational”sub-grouping.where

istherangeofsubgroupj,Nthenumberofsubgroups,andd2*dependsonthenumberNofsubgroupsandthesizenofasubgroup(seenextslide)WhatMeasurementsCanBeUsedtoDescribeProcessvariation?d2*valuesforSSTWhere:N=no.ofsub-groups,n=no.ofsamplesineachsub-groupd2*d2Typical:N=20&n=5

x3

x2

x1

x10x_tExample:WhatMeasurementsCanBeUsedtoDescribeProcessvariation?TheDifferenceBetweenSSTandsLT!!meanTimeDimensionShorttermStandardDeviationLongtermStandardDeviationSubgroupsizen=5NumberofsubgroupsN=7TRENDSubgroupNo.1ThedifferencebetweenthestandarddeviationssLTandsSTgivesanindicationofhowmuchbetteronecandowhenusingappropriateproductioncontrol,likeStatisticalProcessControl(SPC).Short-termstandarddeviation:Long-termstandarddeviation

:ThedifferencebetweensSTandsLTThedifferencebetweensSTandsLTThedifferencebetweensLTandsST

isonlyinthewaythatthestandarddeviationiscalculatedsLTisalwaysthesameorlargerthansSTIfsLTequalssST,thentheprocesscontroloverthelonger-termisthesameastheshort-term,andtheprocesswouldnotbenefitfromSPCIfsLTislargerthansST,thentheprocesshaslostcontroloverthelonger-term,andtheprocesswouldbenefitfromSPCThereliabilityofsLTisimprovedifthedataistakenoveralongerperiodoftime.AlternativelysLTcanbecalculatedonseveraloccasionsseparatedbytimeandtheresultscomparedtoseewhethersLTisstableExercise1:SampleDistributions1.InExcelfile"Dataexercise1.xls"

youfind100measurementsbeingtheresultofacapabilitystudy.Thespecificationforthedimensionis15,16,01

2.Howwelldoesthesamplepopulationfitthespecification,e.g.shouldweexpectanypartsoutsidespec?3.Mentionpossibleconsequencesofhavingapartoutsidespec.4.Mentionpossiblecausesofvariationforparts.5. Calculatethesamplemeanandsamplestandarddeviationforthe100measurements.UsetheaverageandstdevfunctionsExcel.Section3.CpandCpkConceptDefiningCpandPpSamplemeanProcessvariation6*s

USL-LSLLSL

USLNominaldimThetoleranceareadividedbythetotalprocessvariation,irrespectiveofprocesscentring.DefiningCpkandPpkSamplemeanProcessvariation3sProcessvariation3sMean-LSLUSL-MeanLSL

USLNominaldimCpkandPpkIndexesaccountalsoforprocesscentring.WhatistheDifferenceBetweenCpandCpk?TheCpindexonlyaccountsforprocessvariabilityTheCpkIndexaccountsforprocessvariabilityandcenteringoftheprocessmeantothedesignnominalTherefore,Cp

CpkNOTE:SameappliesalsoforPpandPpkCp=Cpk(bothlow)LSLUSLMean=NominalRejectpartsRejectpartsCphigh,Cpklow

Processshouldbeoptimized!NominalLSLMeanUSLRejectpartsWhatDoTheseIndexesTellUs??Simplenumericalvaluestodescribethequalityoftheprocess>>ThehigherthenumberthebetterRequirementforCpandCpkis1.67min.RecommendationforPpandPpk

is1.33min.Thisleavesussomespaceforthevariation,i.e.asafetymarginAreweabletoimproveourprocessbyusingSPC?Ifindexislow,followingthingsshouldbegivenathought:IstheproductdesignOK?Aretolerancelimitssetcorrectly?Tootight?Istheprocesscapableofproducinggoodqualityproducts?Processvariation?DOErequired?Isthemeasuringsystemcapable?(SeeGageR&R)Cpk

-Witha2-sigmasafetymargin-3sST+3sSTLCLUCLLSLUSLMeanvalue=NominalvalueorTargetRequirementforCpandCpkis