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OperationsManagement Supplement6 StatisticalProcessControl 2006PrenticeHall Inc PowerPointpresentationtoaccompanyHeizer RenderPrinciplesofOperationsManagement 6eOperationsManagement 8e Outline Outline Continued ProcessCapabilityProcessCapabilityRatio Cp ProcessCapabilityIndex Cpk AcceptanceSamplingOperatingCharacteristicCurveAverageOutgoingQuality LearningObjectives Whenyoucompletethissupplement youshouldbeableto IdentifyorDefine LearningObjectives Whenyoucompletethissupplement youshouldbeableto IdentifyorDefine LCLandUCLP chartsandc chartsCpandCpkAcceptancesamplingOCcurve LearningObjectives Whenyoucompletethissupplement youshouldbeableto IdentifyorDefine AQLandLTPDAOQProducer sandconsumer srisk LearningObjectives Whenyoucompletethissupplement youshouldbeableto DescribeorExplain Theroleofstatisticalqualitycontrol VariabilityisinherentineveryprocessNaturalorcommoncausesSpecialorassignablecausesProvidesastatisticalsignalwhenassignablecausesarepresentDetectandeliminateassignablecausesofvariation StatisticalProcessControl SPC NaturalVariations AlsocalledcommoncausesAffectvirtuallyallproductionprocessesExpectedamountofvariationOutputmeasuresfollowaprobabilitydistributionForanydistributionthereisameasureofcentraltendencyanddispersionIfthedistributionofoutputsfallswithinacceptablelimits theprocessissaidtobe incontrol AssignableVariations AlsocalledspecialcausesofvariationGenerallythisissomechangeintheprocessVariationsthatcanbetracedtoaspecificreasonTheobjectiveistodiscoverwhenassignablecausesarepresentEliminatethebadcausesIncorporatethegoodcauses Samples Tomeasuretheprocess wetakesamplesandanalyzethesamplestatisticsfollowingthesesteps a Samplesoftheproduct sayfiveboxesofcerealtakenoffthefillingmachineline varyfromeachotherinweight FigureS6 1 Samples Tomeasuretheprocess wetakesamplesandanalyzethesamplestatisticsfollowingthesesteps b Afterenoughsamplesaretakenfromastableprocess theyformapatterncalledadistribution FigureS6 1 Samples Tomeasuretheprocess wetakesamplesandanalyzethesamplestatisticsfollowingthesesteps c Therearemanytypesofdistributions includingthenormal bell shaped distribution butdistributionsdodifferintermsofcentraltendency mean standarddeviationorvariance andshape FigureS6 1 Samples Tomeasuretheprocess wetakesamplesandanalyzethesamplestatisticsfollowingthesesteps d Ifonlynaturalcausesofvariationarepresent theoutputofaprocessformsadistributionthatisstableovertimeandispredictable FigureS6 1 Samples Tomeasuretheprocess wetakesamplesandanalyzethesamplestatisticsfollowingthesesteps e Ifassignablecausesarepresent theprocessoutputisnotstableovertimeandisnotpredicable FigureS6 1 ControlCharts Constructedfromhistoricaldata thepurposeofcontrolchartsistohelpdistinguishbetweennaturalvariationsandvariationsduetoassignablecauses TypesofData CharacteristicsthatcantakeanyrealvalueMaybeinwholeorinfractionalnumbersContinuousrandomvariables Variables Attributes Defect relatedcharacteristicsClassifyproductsaseithergoodorbadorcountdefectsCategoricalordiscreterandomvariables CentralLimitTheorem Regardlessofthedistributionofthepopulation thedistributionofsamplemeansdrawnfromthepopulationwilltendtofollowanormalcurve ProcessControl FigureS6 2 PopulationandSamplingDistributions Distributionofsamplemeans FigureS6 3 SamplingDistribution FigureS6 4 StepsInCreatingControlCharts TakesamplesfromthepopulationandcomputetheappropriatesamplestatisticUsethesamplestatistictocalculatecontrollimitsanddrawthecontrolchartPlotsampleresultsonthecontrolchartanddeterminethestateoftheprocess inoroutofcontrol InvestigatepossibleassignablecausesandtakeanyindicatedactionsContinuesamplingfromtheprocessandresetthecontrollimitswhennecessary ControlChartsforVariables SettingChartLimits SettingControlLimits For99 73 controllimits z 3 SettingControlLimits ControlChartforsampleof9boxes SettingChartLimits ControlChartFactors TableS6 1 SettingControlLimits SettingControlLimits SettingControlLimits R Chart TypeofvariablescontrolchartShowssamplerangesovertimeDifferencebetweensmallestandlargestvaluesinsampleMonitorsprocessvariabilityIndependentfromprocessmean SettingChartLimits ForR Charts SettingControlLimits MeanandRangeCharts FigureS6 5 MeanandRangeCharts FigureS6 5 AutomatedControlCharts ControlChartsforAttributes ForvariablesthatarecategoricalGood bad yes no acceptable unacceptableMeasurementistypicallycountingdefectivesChartsmaymeasurePercentdefective p chart Numberofdefects c chart ControlLimitsforp Charts Populationwillbeabinomialdistribution butapplyingtheCentralLimitTheoremallowsustoassumeanormaldistributionforthesamplestatistics p ChartforDataEntry p ChartforDataEntry p ChartforDataEntry Possibleassignablecausespresent ControlLimitsforc Charts PopulationwillbeaPoissondistribution butapplyingtheCentralLimitTheoremallowsustoassumeanormaldistributionforthesamplestatistics c ChartforCabCompany PatternsinControlCharts Normalbehavior Processis incontrol FigureS6 7 PatternsinControlCharts Oneplotoutabove orbelow Investigateforcause Processis outofcontrol FigureS6 7 PatternsinControlCharts Trendsineitherdirection 5plots Investigateforcauseofprogressivechange FigureS6 7 PatternsinControlCharts Twoplotsverynearlower orupper control Investigateforcause FigureS6 7 PatternsinControlCharts Runof5above orbelow centralline Investigateforcause FigureS6 7 PatternsinControlCharts Erraticbehavior Investigate FigureS6 7 WhichControlCharttoUse VariablesData WhichControlCharttoUse Usingthep chart ObservationsareattributesthatcanbecategorizedintwostatesWedealwithfraction proportion orpercentdefectivesHaveseveralsamples eachwithmanyobservations AttributeData WhichControlCharttoUse Usingac Chart ObservationsareattributeswhosedefectsperunitofoutputcanbecountedThenumbercountedisoftenasmallpartofthepossibleoccurrencesDefectssuchasnumberofblemishesonadesk numberoftyposinapageoftext flawsinaboltofcloth AttributeData ProcessCapability ThenaturalvariationofaprocessshouldbesmallenoughtoproduceproductsthatmeetthestandardsrequiredAprocessinstatisticalcontroldoesnotnecessarilymeetthedesignspecificationsProcesscapabilityisameasureoftherelationshipbetweenthenaturalvariationoftheprocessandthedesignspecifications ProcessCapabilityRatio AcapableprocessmusthaveaCpofatleast1 0DoesnotlookathowwelltheprocessiscenteredinthespecificationrangeOftenatargetvalueofCp 1 33isusedtoallowforoff centerprocessesSixSigmaqualityrequiresaCp 2 0 ProcessCapabilityRatio Insuranceclaimsprocess ProcessCapabilityRatio Insuranceclaimsprocess ProcessCapabilityRatio Insuranceclaimsprocess Processiscapable ProcessCapabilityIndex AcapableprocessmusthaveaCpkofatleast1 0Acapableprocessisnotnecessarilyinthecenterofthespecification butitfallswithinthespecificationlimitatbothextremes ProcessCapabilityIndex NewCuttingMachine ProcessCapabilityIndex NewCuttingMachine ProcessCapabilityIndex NewCuttingMachine NewmachineisNOTcapable Bothcalculationsresultin InterpretingCpk FigureS6 8 AcceptanceSampling FormofqualitytestingusedforincomingmaterialsorfinishedgoodsTakesamplesatrandomfromalot shipment ofitemsInspecteachoftheitemsinthesampleDecidewhethertorejectthewholelotbasedontheinspectionresultsOnlyscreenslots doesnotdrivequalityimprovementefforts OperatingCharacteristicCurve Showshowwellasamplingplandiscriminatesbetweengoodandbadlots shipments Showstherelationshipbetweentheprobabilityofacceptingalotanditsqualitylevel The Perfect OCCurve AQLandLTPD AcceptableQualityLevel AQL PoorestlevelofqualitywearewillingtoacceptLotTolerancePercentDefective LTPD Qualitylevelweco