ToolsforManagersStatisticalProcessControlProfessorStephenR LawrenceCollegeofBusinessandAdministrationGraduateSchoolofBusinessAdministrationUniversityofColoradoDenver Colorado CausesofVariation NaturalCauses AssignableCauses Whatpreventsperfection Processvariation InherenttoprocessRandomCannotbecontrolledCannotbepreventedExamplesweatheraccuracyofmeasurementscapabilityofmachine CausesofVariation NaturalCauses AssignableCauses Whatpreventsperfection Processvariation ExogenoustoprocessNotrandomControllablePreventableExamplestoolwear Monday effectpoormaintenance InherenttoprocessRandomCannotbecontrolledCannotbepreventedExamplesweatheraccuracyofmeasurementscapabilityofmachine ProductSpecificationandProcessVariation Productspecificationdesiredrangeofproductattributepartofproductdesignlength weight thickness color nominalspecificationupperandlowerspecificationlimitsProcessvariabilityinherentvariationinprocesseslimitswhatcanactuallybeachieveddefinesandlimitsprocesscapabilityProcessmaynotbecapableofmeetingspecification ProcessCapability LSL USL Spec CapableprocessVerycapableprocessProcessnotcapable Processvariation ProcessCapabilityIndexI Measureofcapabilityofprocesstomeet fallwithin specificationlimits ProcessCapabilityIndexI Measureofcapabilityofprocesstomeet fallwithin specificationlimitsTake width ofprocessvariationas6 LSL USL Spec 6 3 ProcessCapabilityIndexI Measureofcapabilityofprocesstomeet fallwithin specificationlimitsTake width ofprocessvariationas6 LSL USL Spec 6 3 99 7 ProcessCapabilityIndexI Measureofcapabilityofprocesstomeet fallwithin specificationlimitsTake width ofprocessvariationas6 If6 USL LSL thenatleast99 7 ofoutputofprocesswillfallwithinspecificationlimits LSL USL Spec 6 3 99 7 ProcessCapabilityIndexII DefineProcessCapabilityIndexCpas IfCp 1 0 processis capableIfCp 1 0 processis notcapable ProcessCapability Example Amanufacturerofgranolabarshasaweightspecification2ouncesplusorminus0 05ounces Ifthestandarddeviationofthebar makingmachineis0 02ounces istheprocesscapable ProcessCapability Example Amanufacturerofgranolabarshasaweightspecification2ouncesplusorminus0 05ounces Ifthestandarddeviationofthebar makingmachineis0 02ounces istheprocesscapable USL 2 0 05 2 05ounces ProcessCapability Example Amanufacturerofgranolabarshasaweightspecification2ouncesplusorminus0 05ounces Ifthestandarddeviationofthebar makingmachineis0 02ounces istheprocesscapable USL 2 0 05 2 05ouncesLSL 2 0 05 1 95ounces ProcessCapability Example Amanufacturerofgranolabarshasaweightspecification2ouncesplusorminus0 05ounces Ifthestandarddeviationofthebar makingmachineis0 02ounces istheprocesscapable USL 2 0 05 2 05ouncesLSL 2 0 05 1 95ouncesCp USL LSL 6 2 05 1 95 6 0 02 0 1 0 12 0 85 ProcessCapability Example Amanufacturerofgranolabarshasaweightspecification2ouncesplusorminus0 05ounces Ifthestandarddeviationofthebar makingmachineis0 02ounces istheprocesscapable USL 2 0 05 2 05ouncesLSL 2 0 05 1 95ouncesCp USL LSL 6 2 05 1 95 6 0 02 0 1 0 12 0 85 Therefore theprocessisnotcapable ProcessCentering LSL USL Spec CapableandcenteredCapablebutnotcenteredCapablebutnotcentered ProcessCentering Example Forthegranolabarmanufacturer iftheprocessisincorrectlycenteredat2 05insteadof2 00ounces whatfractionofbarswillbeoutofspecification ProcessCentering Example Forthegranolabarmanufacturer iftheprocessisincorrectlycenteredat2 05insteadof2 00ounces whatfractionofbarswillbeoutofspecification 2 0 LSL 1 95 USL 2 05 ProcessCentering Example Forthegranolabarmanufacturer iftheprocessisincorrectlycenteredat2 05insteadof2 00ounces whatfractionofbarswillbeoutofspecification 2 0 LSL 1 95 USL 2 05 ProcessCentering Example Forthegranolabarmanufacturer iftheprocessisincorrectlycenteredat2 05insteadof2 00ounces whatfractionofbarswillbeoutofspecification Outofspec ProcessCentering Example Forthegranolabarmanufacturer iftheprocessisincorrectlycenteredat2 05insteadof2 00ounces whatfractionofbarswillbeoutofspecification 50 ofproductionwillbeoutofspecification Outofspec Example ProcessCapability ProcessControlCharts EstablishcapabilityofprocessundernormalconditionsUsenormalprocessasbenchmarktostatisticallyidentifyabnormalprocessbehaviorCorrectprocesswhensignsofabnormalperformancefirstbegintoappearControltheprocessratherthaninspecttheproduct Statisticaltechniquefortrackingaprocessanddeterminingifitisgoing outtocontrol ProcessControlChartsTheoryI UpperSpecLimit LowerSpecLimit TargetSpec ProcessControlChartsTheoryI UpperSpecLimit LowerSpecLimit 6 3 TargetSpec ProcessControlChartsTheoryI UpperSpecLimit LowerSpecLimit UpperControlLimit LowerControlLimit 6 3 TargetSpec ProcessControlChartsTheoryII UpperControlLimit UCL LowerControlLimit LCL 6 3 NaturalVariation ProcessControlChartsPractice UCL Target LCL Time Samples ProcessControlCharts Practice UCL Target LCL Samples Time Naturalvariation ProcessControlCharts Practice UCL Target LCL Samples Time Incontrol Naturalvariation ProcessControlCharts Practice UCL Target LCL Samples Time Incontrol Naturalvariation ProcessControlCh