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CHAPTER10QualityControlMcGraw-Hill/IrwinOperationsManagement,EighthEdition,byWilliamJ.StevensonCopyright?2005byTheMcGraw-HillCompanies,Inc.Allrightsreserved.PhasesofQualityAssuranceAcceptancesamplingProcesscontrolContinuousimprovementInspectionbefore/afterproductionInspectionandcorrectiveactionduringproductionQualitybuiltintotheprocessTheleastprogressiveThemostprogressiveFigure10.1InspectionHowMuch/HowOftenWhere/WhenCentralizedvs.On-siteInputsTransformationOutputsAcceptancesamplingProcesscontrolAcceptancesamplingFigure10.2CostOptimalAmountofInspectionInspectionCostsCostof
inspectionCostof
passingdefectivesTotalCostFigure10.3WheretoInspectintheProcessRawmaterialsandpurchasedpartsFinishedproductsBeforeacostlyoperationBeforeanirreversibleprocessBeforeacoveringprocessExamplesofInspectionPointsTable10.1StatisticalProcessControl:
StatisticalevaluationoftheoutputofaprocessduringproductionQualityofConformance:
AproductorserviceconformstospecificationsControlChartControlChartPurpose:tomonitorprocessoutputtoseeifitisrandomAtimeorderedplotrepresentativesamplestatisticsobtainedfromanongoingprocess(e.g.samplemeans)UpperandlowercontrollimitsdefinetherangeofacceptablevariationControlChart0123456789101112131415UCLLCLSamplenumberMeanOutof
controlNormalvariation
duetochanceAbnormalvariation
duetoassignablesourcesAbnormalvariation
duetoassignablesourcesFigure10.4StatisticalProcessControlTheessenceofstatisticalprocesscontrolistoassurethattheoutputofaprocessisrandomsothatfutureoutputwillberandom.StatisticalProcessControlTheControlProcessDefineMeasureCompareEvaluateCorrectMonitorresultsStatisticalProcessControlVariationsandControlRandomvariation:Naturalvariationsintheoutputofaprocess,createdbycountlessminorfactorsAssignablevariation:AvariationwhosesourcecanbeidentifiedSamplingDistributionSampling
distributionProcess
distributionMeanFigure10.5NormalDistributionMean
95.44%99.74%
StandarddeviationFigure10.6ControlLimitsSampling
distributionProcess
distributionMeanLower
control
limitUpper
control
limitFigure10.7SPCErrorsTypeIerrorConcludingaprocessisnotincontrolwhenitactuallyis.TypeIIerrorConcludingaprocessisincontrolwhenitisnot.TypeIErrorMeanLCLUCL
/2
/2
Probability
ofTypeIerrorFigure10.8ObservationsfromSampleDistributionSamplenumberUCLLCL1234Figure10.9ControlChartsforVariablesMeancontrolchartsUsedtomonitorthecentraltendencyofaprocess.XbarchartsRangecontrolchartsUsedtomonitortheprocessdispersionRchartsVariablesgeneratedatathataremeasured.MeanandRangeChartsUCLLCLUCLLCLR-chartx-ChartDetectsshiftDoesnot
detectshiftFigure10.10A(processmeanisshiftingupward)SamplingDistributionx-ChartUCLDoesnot
revealincreaseMeanandRangeChartsUCLLCLLCLR-chartRevealsincreaseFigure10.10B(processvariabilityisincreasing)SamplingDistributionControlChartforAttributesp-Chart-Controlchartusedtomonitortheproportionofdefectivesinaprocessc-Chart-ControlchartusedtomonitorthenumberofdefectsperunitAttributesgeneratedatathatarecounted.Useofp-ChartsWhenobservationscanbeplacedintotwocategories.GoodorbadPassorfailOperateordon’toperateWhenthedataconsistsofmultiplesamplesofseveralobservationseachTable10.3Useofc-ChartsUseonlywhenthenumberofoccurrencesperunitofmeasurecanbecounted;non-occurrencescannotbecounted.Scratches,chips,dents,orerrorsperitemCracksorfaultsperunitofdistanceBreaksorTearsperunitofareaBacteriaorpollutantsperunitofvolumeCalls,complaints,failuresperunitoftimeTable10.3UseofControlChartsAtwhatpointintheprocesstousecontrolchartsWhatsizesamplestotakeWhattypeofcontrolcharttouseVariablesAttributesRunTestsRuntest–atestforrandomnessAnysortofpatterninthedatawouldsuggestanon-randomprocessAllpointsarewithinthecontrollimits-theprocessmaynotberandomNonrandomPatternsinControlchartsTrendCyclesBiasMeanshiftToomuchdispersionFigure10.11CountingAbove/BelowMedianRuns (7runs)CountingUp/DownRuns (8runs)UUD
UDUDUUDBAABABBBAABFigure10.12Figure10.13
CountingRunsTolerancesorspecificationsRangeofacceptablevaluesestablishedbyengineeringdesignorcustomerrequirementsProcessvariabilityNaturalvariabilityinaprocessProcesscapabilityProcessvariabilityrelativetospecification
ProcessCapability
ProcessCapabilityLower
SpecificationUpper
SpecificationA.Processvariability
matchesspecificationsLower
SpecificationUpper
SpecificationB.Processvariability
wellwithinspecificationsLower
SpecificationUpper
SpecificationC.Processvariability
exceedsspecificationsFigure10.15ProcessCapabilityRatioProcesscapabilityratio,Cp=specificationwidthprocesswidthUpperspecification–lowerspecification6
Cp=Process
meanLower
specificationUpper
specification1350ppm1350ppm1.7ppm1.7ppm+/-3Sigma+/-6Sigma3Sigmaand6SigmaQualityImprovingProcessCapabilitySimplifyStandardizeMistake-proofUpgradeequipmentAutomateTaguchiLossFunctionCostTargetLower
specUpper
specTraditional
costfunctionTaguchi
costfunctionFigure10.17LimitationsofCapabilityIndexesProcessmaynotbestableProcessoutputmaynotbenormallydistributedProcessnotcenteredbutCpisusedAdditionalPowerPointslides
contributedby
GeoffWillis,
UniversityofCentralOklahoma.CHAPTER10StatisticalProcessControl(SPC)InventedbyWalterShewhartatWesternElectricDistinguishesbetweencommoncausevariability(random)specialcausevariability(assignable)BasedonrepeatedsamplesfromaprocessEmpiricalRule-3
-1
-2
+1
+2
+3
68%95%99.7%ControlChartsinGeneralArenamedaccordingtothestatisticsbeingplotted,i.e.,Xbar,R,p,andcHaveacenterlinethatistheoverallaverageHavelimitsaboveandbelowthecenterlineat±3standarddeviations(usually)CenterlineLowerControlLimit(LCL)UpperControlLimit(UCL)VariablesDataChartsProcessCenteringXbarchartXbarisasamplemeanProcessDispersion(consistency)RchartRisasamplerangeXbarchartsCenterlineisthegran
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