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ProcessCapability Cp Cpk Pp Ppk GlobalTrainingMaterial Creator GlobalMechanicsProcessManagerFunction MechanicsApprover GaryBradley GlobalProcessTeamDocumentID DMT00018 ENVersion Status V 1 0 ApprovedLocation Notes NMP DOCMANR4 PCP PCProcessLibraryDocManChangeHistory IssueDateHandledByComments1 021stDec 01JimChristy S renLundsfrydApprovedforGlobalUseNOTE Allcommentsandimprovementsshouldbeaddressedtothecreatorofthisdocument Contents SectionHeading DescriptionPage1Variation TolerancesandDimensionalControl42Population SampleandNormalDistribution153CpandCpkConcept284UseoftheNMPDataCollectionSpreadsheet445ConfidenceofCpk52 ProcessCapability EvaluatingManufacturingVariation AcknowledgementsBennyMatthiassen NMPCMT Copenhagen Denmark FrankAdler NMPAlliance Dallas USA JoniLaakso NMPR D Salo Finland JimChristy NMPSRC Southwood UK Section1Variation TolerancesandDimensionalControl TwoTypesofProductCharacteristics Variable Acharacteristicmeasuredinphysicalunits e g millimetres volts amps decibelandseconds Inthistrainingwedealwithvariablesonly TheSourcesofProcess SystemVariation Process TwoTypesofProcesses Allprocesseshave Natural random variability duetocommoncauses StableProcess Aprocessinwhichvariationinoutcomesarisesonlyfromcommoncauses UnstableProcess Aprocessinwhichvariationisaresultofbothcommonandspecialcauses Unnaturalvariability duetospecialcauses Shewhart 1931 TheTwoCausesofVariation CommonCauses Causesthatareimplementedintheprocessduetothedesignoftheprocess andaffectalloutcomesoftheprocessIdentifyingthesetypesofcausesrequiresmethodssuchasDesignofExperiment DOE etc SpecialCauses Causesthatarenotpresentintheprocessallthetimeanddonotaffectalloutcomes butarisebecauseofspecificcircumstancesSpecialcausescanbeidentifiedusingStatisticalProcessControl SPC Defect USL LSL nominalvalue Tolerances LSL lowerspecificationlimit 10 7 USL upperspecificationlimit 10 9 Acceptablepart RejectedPart RejectedProduct Nominal10 8 0 1 RejectedPart Atoleranceisaallowedmaximumvariationofadimension MeasurementReport Inmostcaseswemeasureonlyonepartpercavityformeasurementreport ExampleofCapabilityAnalysisData Forsomecriticaldimensionsweneedtomeasuremorethan1partForcapabilitydataweusuallymeasure5pcs2times hour 100pcs butsamplingplanneedstobemadeonthebasisofproductionquantity rundurationandcycletime ProcessCapability Whatisit ProcessCapabilityisameasureoftheinherentcapabilityofamanufacturingprocesstobeabletoconsistentlyproducecomponentsthatmeettherequireddesignspecifications ProcessCapabilityisdesignatedbyCpandCpk ProcessPerformanceisameasureoftheperformanceofaprocesstobeabletoconsistentlyproducecomponentsthatmeettherequireddesignspecifications ProcessPerformanceincludesspecialcausesofvariationnotpresentinProcessCapability ProcessPerformanceisdesignatedPpandPpk WhyMakeProcessCapabilityStudies Aprocesscapabilitystudywouldrevealthatthetoolshouldnotbeaccepted Whenadimensionneedstobekeptproperlywithinspec wemuststudytheprocesscapability butstillthisisnoguaranteefortheactualperformanceoftheprocessasitisonlyaninitialcapabilitystudy TheNokiaProcessVerificationProcess Section2 Population SampleandNormalDistribution TheBellShaped Normal Distribution Symmetricalshapewithapeakinthemiddleoftherangeofthedata Indicatesthattheinputvariables X s totheprocessarerandomlyinfluenced PopulationParameters Populationmean Populationstandarddeviation PopulationversusSample PopulationAnentiregroupofobjectsthathavebeenmadeorwillbemadecontainingacharacteristicofinterest SampleThegroupofobjectsactuallymeasuredinastatisticalstudyAsampleisusuallyasubsetofthepopulationofinterest TheNormalDistribution WhatMeasurementsCanBeUsedtoDescribeaProcessorSystem mean average ordescribesthelocationofthedistribution m ameasureofcentraltendency isthemeanoraverageofallvaluesinthepopulation Whenonlyasampleofthepopulationisbeingdescribed meanismoreproperlydenotedas x bar Themostsimplemeasureofvariabilityistherange Therangeofasampleisdefinedbyasthedifferencebetweenthelargestandthesmallestobservationfromsamplesinasub group e g 5consecutivepartsfromthemanufacturingprocess WhatMeasurementsCanBeUsedtoDescribeProcessvariation sST oftennotatedas orsigma isanothermeasureofdispersionorvariabilityandstandsfor short termstandarddeviation whichmeasuresthevariabilityofaprocessorsystemusing rational sub grouping whereistherangeofsubgroupj Nthenumberofsubgroups andd2 dependsonthenumberNofsubgroupsandthesizenofasubgroup seenextslide WhatMeasurementsCanBeUsedtoDescribeProcessvariation d2 valuesforSST Example WhatMeasurementsCanBeUsedtoDescribeProcessvariation TheDifferenceBetweenSSTandsLT ThedifferencebetweenthestandarddeviationssLTandsSTgivesanindicationofhowmuchbetteronecandowhenusingappropriateproductioncontrol likeStatisticalProcessControl SPC Short termstandarddeviation Long termstandarddeviation ThedifferencebetweensSTandsLT ThedifferencebetweensSTandsLT ThedifferencebetweensLTandsSTisonlyinthewaythatthestandarddeviationiscalculatedsLTisalwaysthesameorlargerthansSTIfsLTequalssST thentheprocesscontroloverthelonger termisthesameastheshort term andtheprocesswouldnotbenefitfromSPCIfsLTislargerthansST thentheprocesshaslostcontroloverthelonger term andtheprocesswouldbenefitfromSPCThereliabilityofsLTisimprovedifthedataistakenoveralongerperiodoftime AlternativelysLTcanbecalculatedonseveraloccasionsseparatedbytimeandtheresultscomparedtoseewhethersLTisstable Exercise1 SampleDistributions 1 InExcelfile Dataexercise1 xls youfind100measurementsbeingtheresultofacapabilitystudy Thespecificationforthedimensionis15 16 012 Howwelldoesthesamplepopulationfitthespecification e g shouldweexpectanypartsoutsidespec 3 Mentionpossibleconsequencesofhavingapartoutsidespec 4 Mentionpossiblecausesofvariationforparts 5 Calculatethesamplemeanandsamplestandarddeviationforthe100measurements UsetheaverageandstdevfunctionsExcel Section3 CpandCpkConcept DefiningCpandPp Thetoleranceareadividedbythetotalprocessvariation irrespectiveofprocesscentring DefiningCpkandPpk CpkandPpkIndexesaccountalsoforprocesscentring WhatistheDifferenceBetweenCpandCpk TheCpindexonlyaccountsforprocessvariabilityTheCpkIndexaccountsforprocessvariabilityandcenteringoftheprocessmeantothedesignnominalTherefore Cp CpkNOTE SameappliesalsoforPpandPpk WhatDoTheseIndexesTellUs Simplenumericalvaluestodescribethequalityoftheprocess Thehigherthenumberthebetter RequirementforCpandCpkis1 67min RecommendationforPpandPpkis1 33min Thisleavesussomespaceforthevariation i e asafetymargin AreweabletoimproveourprocessbyusingSPC Ifindexislow followingthingsshouldbegivenathought IstheproductdesignOK Aretolerancelimitssetcorrectly Tootight Istheprocesscapableofproducinggoodqualityproducts Processvariation DOErequired Isthemeasuringsystemcapable SeeGageR R Cpk Witha2 sigmasafetymargin RequirementforCpandCpkis1 67min 1 67isaratioof 5 3or10 6 2 standarddeviation 2 standarddeviation Cpk 1 67theprocessNOTCAPABLE AcceptabilityofCpkIndex Cpk 1 67theprocessisCAPABLE Cpk 2 0theprocesshasreachedSixSigmalevel WhatDoTheseIndexesTellUs IfCp Cpk IfPp Ppk IfCpk Cp IfPpk Pp IfCp Pp IfCpk Ppk IfPp Cp IfPpk Cpk thenprocessisaffectedbyspecialcauses InvestigateX bar R chartforout of controlconditions SPCmaybeeffective thenprocessisnotaffectedbyspecialcausesduringthestudyrun SPCwouldnotbeeffectiveinthiscase thenprocessperfectlycentred thenprocessnotcentred checkprocessmeanagainstdesignnominal CpandCpkIndicesandDefects bothtailsofthenormaldistribution Pp Ppk 1 33 63ppmdefects 0 006 Cp Cpk 1 67 0 6ppmdefects 0 00006 Note PpmrejectratescalculatedfromCp Cpkarebasedontheshorttermvariationwhichmaynotrepresentthelongtermrejectrate TheEffectsofCpkandCponFFR Exercise2 CpandCpk CalculateCpandCpkforthe100measurementsinthefile Dataexercise1 xls DeterminetheapproximateCpandCpkforthe4samplepopulationsonthefollowingpageShouldactionsbemadetoimprovetheseprocesses Ifyes which EstimateCpandCpk Thewidthofthenormaldistributionsshowninclude 3 s EstimateCpandCpk A LSL USL A Meanandnominal USL LSL 6 s USL Mean Mean LSL 3 s EstimateCpandCpk B LSL USL B Nominal Mean USL LSL 6 s USL Mean Mean LSL 3 s EstimateCpandCpk C LSL USL C Nominal Mean USL LSL 6 s USL Mean Mean LSL 3 s EstimateCpandCpk D USL LSL D Nominal Mean USL LSL 6 s USL Mean Mean LSL 3 s Section4 UseoftheNMPDataCollectionSpreadsheet ExampleofhowtoCollectData 1 Runinandstabiliseprocess2 Notethemainparametersforreference3 Whentheprocessisstablerunthetoolfor10hours3 Take5partsoutfromeachcavityeveryhalfhourandmarkthemwithtime dateandcavity Total20setsof5partsfromeachcavitymustbemade oraccordingtoagreement 4 Afterthelastsamplelotnotethemainprocessparametersforreference5 Measureandrecordthemainfunctionalcharacteristics whitediamonds 6 FilldataintotheNMPdatacollectionspreadsheet7 Analyse SeeDMY00019 ENClassificationandMarkingofFunctionalCharacteristics DataCollectionSheet