StatisticalProcessControl(SPC).ppt

Module3 StatisticalProcessControl SPC Methodology 2 PCSElements CreateMeasurementPlan EstablishMonitor SPC ImplementResponseFlowChecklist RFC Element1 Element2 Element3 3 Contents IntroductionWhatisSPCWhatisStabilityWhatisaControlChartHowtoSet upaControlChartTypeofControlChartsAvailableHowtoCalculatetheControlLimitsSPCTrendRulesWhentoReviseControlLimitsProcessCapabilityStudySpeclimitsVSControlLimitsStabilityVSCapabilityControlChartReduction EliminationSPCExpectations 4 WhatisSPC StatisticalAnythingthatdealswiththecollection analysis interpretation presentationofnumericaldataGaininginformationformakinginformeddecisionsProcessCombinationofmachines tools methods materials peopleemployedtoattainprocessspecificationAsimilarprocedure eventthatishappeningrepetitivelyControlTokeepsomethingwithinadesiredconditionMakesomethingbehavethewaywewantittobehave Theuseofstatisticaltechniquessuchascontrolchartstoanalyzeaprocess takeappropriateactionstoachieve maintainastableprocess improveprocesscapability 5 WhatisStability AprocessissaidtobeStableifithasthefollowingproperties PatternappearsrandomConstantprocessmeanUniformvariabilityovertimeNotrends runs shifts erraticups downsImportantformanyreasons Increasedproductivityofengineering manufacturingpersonnelPredictable repeatableresultswithinaspecifiedrange 6 WhatisaControlChart AtrendchartwithcontrollimitsGraphicalrepresentationofprocessperformance wheredataiscollectedatregulartimesequenceofproductionValuabletoolfordifferentiatingbetweencommoncauseandspecialcausevariationEvaluatingwhetheraprocessisorisnotinastateofstatisticalcontrolItletsthedata talk byitself basisfordata drivendecisions 7 ControlLimits Atypicalcontrolchartconsistsofthreelines CL Theaverage measureoflocation processperformancewhentheprocessisin controlUCL LCL Therangeof usual processperformancewhentheprocessisstable Linesdrawn3standarddeviations 3sigma oneachsideofthecenterline 8 ControlChartAssumptions ProcessStabilityTheprocessmustbeinstatisticalcontrolNormalityTheunderlyingprocessdistributionisnormalNote Iftheassumptionsarenotmet thecontrollimitscalculatedaremisleading donotaccuratelyindicate3sigmacontrollimits Seeyoursitestatisticianforadviceoncalculationmethodswhenassumptionsareviolated 9 TestforControlChartAssumptions ProcessStability nooutliers Screenoutoutliersfromthedatabasebeforecomputingfinalcontrollimitsbyusingacontrolchart Anypointbeyondeithercontrollimitisanoutlier Reportnumberofoutliersscreened NormalityPlotanormalprobabilityplotofthedataoroverlayanormalcurveoverthehistogram Normallydistributeddatawillroughlyfallonastraightline TestfornormalitybyusingShapiro WilkWtestinJMP 10 SelectappropriatetypeofcontrolcharttobeusedGatherdatatoestablishthecontrolchart Aminimumof30subgroupsisrequiredoveratimeframeasdeterminedbythesamplingplan PlotthedataintimeorderonaTrendChart HowtoSet upaControlChart 11 Computethecontrollimits plotthemonthetrendchartOutliersidentification exclusionExcludetheOut ofControl OOC pointsoroutliersforwhichthereareverified confirmedspecialcausesfromthechartRe computethecontrollimits excludingtheOOCpointsIftherearefewerthan30pointsremainingatanytime collectmoredata It sveryimportantthatthecontrollimitsarecalculatedusingatleast30subgroups HowtoSet upaControlChart Note RefertoAppendixAforControlChartsforLimitedProduction i e 30subgroups 12 Validatethecomputedcontrollimitsagainstdatacollectedbyre plottingthecontrolchartwithdata newcontrollimitsDothelimitsdetectknownproblems Arethelimitstoosensitive Wouldtheyflagproblemsyoudonotknowhowtoreactto UsethecontrollimitsestablishedtomonitorthecriticalparameteridentifiedForeachparameter everymachineshouldhaveaseparatecontrolchartwithseparatelycomputedcontrollimits HowtoSet upaControlChart 13 ControlChartClassifications ClassificationsofcontrolchartsaredependingonthetypeofdataVariablesdataAcharacteristicmeasuredonacontinuousscaleresultinginanumericalvalueExamples VoidSize BondPullStrength Coplanarity BallHeight etc AttributesdataAcharacteristicmeasuredby ofconforming non conformingtoaspecification Outputisclassifiedaspass failoraccept reject E g BrokenWire LiftedBond FM Chipping BentLead etc Canbeexpressedintermsoffraction percentage countorDPM 14 ControlChart WhentoUse Guidelinesonly X R whensubgroupingofsamplesor Mean Range Chart measurementsisapplicable n 10 X whensubgroupingisnotapplicable Individual duetosingleunitreadingmaytake Chart alongtime unitreadingisextremely expensive etc whenit scommontohavesingle measurementspacedtimeapart X S whensubgroupingofsamplesor Mean Standard measurementsisapplicable Deviation Chart ControlChartsForVariables Note SChartcanalsobeusedforanysubgroupsamplesize n especiallyforautomatedSPCsystemasstandarddeviation s isabetterestimatorforwithinlotvariation n 10 15 WhyMRMethodisusedtodetermineControlLimitsforMean Variability Range StandardDeviation Chart Mostbatchproductionprocesseshavealargerrun to runvariationthanwithin runvariationTraditionalcontrolchartformulasdevelopedinthe20 sbyWalterShewhartconsiderablyunderestimatecontrollimits i e toonarrow 16 Traditionalvs MRMethod Traditionalcontrolchartformulasareused MovingRange MR Methodisused X barControlChart X barControlChart 17 X SChartConcept ConsistsofTwoPortions XChartPlotsthemeanoftheXvaluesinthesampleShowsthechangesofthemeanofonesampletoanotherSChartPlotsthestandarddeviationofasampleShowsthechangesindispersionorprocessvariabilityofonesampletoanother 18 ComputingControlLimitsforX SChart Obtainatleastk 30subgroupsComputetheMeanforeachsubgroupofsizenComputetheStandardDeviationforeachsubgroupComputetheMovingRangeforeachsubgroupmean MRXi Xi Xi 1 ComputetheMovingRangeforeachsubgrouprange MRSi Si Si 1 19 ComputingControllimitsforX RChart ComputetheOverallMean X X1 X2 X3 Xk kComputetheAverageofRange S S1 S2 S3 Sk kComputetheAverageofMovingRangeforthemean MRX MRX2 MRX3 MRX4 MRXk k 1 ComputetheAverageofMovingRangefortherange MRS MRS2 MRS3 MRS4 MRSk k 1 20 ComputetheControlLimits DrawthecontrollimitsonboththeX SchartrespectivelyIfLCL S 0 putas0orN A XChartUCL X X 2 66MRXCL X XLCL X X 2 66MRX ComputingControllimitsforX RChart SChartUCL S S 2 66MRSCL S SLCL S S 2 66MRS 21 Observations Mean MovingRange S D MovingRange Subgroup 1 2 3 4 5 X bar MRX S MR S 1 8 0 7 7 8 1 8 0 7 8 7 92 0 16 2 7 1 6 9 7 4 7 3 7 2 7 18 0 74 0 19 0 03 3 8 0 7 5 7 6 7 8 7 9 7 76 0 58 0 21 0 02 30 7 5 7 8 7 9 7 8 7 6 7 72 0 70 0 16 0 04 Average 7 64 0 68 0 19 0 03 XChartUCL X X 2 66MRX 7 64 2 66 0 68 9 45CL X X 7 64LCL X X 2 66MRX 7 64 2 66 0 68 5 83 ExampleofComputingControlLimitsforX SChart SChartUCL S S 2 66MRS 0 19 2 66 0 03 0 27CL S S 0 55LCL S S 2 66MRS 0 19 2 66 0 03 0 11 22 OpenthedatasetThickness jmp 1 Computethemeanforeachlot SelectSummaryfromtheTablesmenu SelectLotastheGroupvariable HighlightThickness selectMeanfromtheStatisticsmenu Then highlightThickness selectStdDevfromtheStatisticsmenu ClickOK 2 Createanindividualscontrolchartusingthetableoflotmeans ranges SelectControlChartfromtheGraphmenu SelectMean thickness StdDev Thickness astheProcessvariable SelectLotastheSampleLabelvariable Verifyoptionsettings ChartTypeis IR IndividualMeasurementboxisselected MovingRangeboxisnotselected K sigmaisselected andK 3 RangeSpan 2 ClickonOK ExampleofComputingControlLimitsforX SChartusingJMP 23 WARNINGS Group Summarywillsortthenewtableinalphabeticalorderofthegroupingvariable Controlchartsmustalwaysbeplottedintimeorder Therefore ifthesummarytableisnotintimeorder youwillhavetosortthetableincorrecttimeorderbeforemakingthecontrolchart ExampleofComputingControlLimitsforX SChartusingJMP LCL S 0 24 Exercise1 OpenthedatasetExer1 jmp ComputetheX ScontrollimitsusingJMPforleadwidth Whatarethecontrollimits Istheprocessstable 25 InterpretationofX SChart Somespecialcausesofout of controlforXChartChangesinmachinesettingoradjustmentMS to MStechniqueinconsistentChangesinmaterialSChartMachineinneedofrepairoradjustmentNewMSesMaterialsarenotuniform 26 AttributesControlCharts Attributecontrolchartsareusefulwhenitisdifficultorimpracticaltomonitoraprocessnumerically onacontinuousscale AdefectisanindividualfailuretomeetasinglerequirementAdefectiveunitisaunitthatcontainsoneormoredefects 27 ControlChartsForAttributes 28 pChartConcept ItplotsproportionofdefectiveunitsinasampleTheproportionofdefectiveunitsinasamplecanbeintermsoffraction percentordpmItallowsustochartproductionprocesseswheresamplesizecannotbeequal 29 ComputingControlLimitsforpChartwithMR Method Obtainatleastk 30subgroupsorlots Datacollectedin ofunitsinspected ofunitsrejected Computethedefectiveratefromtheithlot i 1 2 k pi ofunitsrejected ofunitsinspectedComputethecontrollimitsusing UCL p p 2 66MRpCL p pLCL p p 2 66MRp WhenLCL 0 putLCL 0orN ADrawthecontrollimitsonpchart 30 Notes TheMR Methoddescribeshowthecontrollimitsarecalculatedassumingequal ornear equal samplesizes Ifthesamplesizesvarybymorethan50 ofeachother youshouldconsultastatistician npChartisapplicablewhenallsubgroupshaveconstantsamplesizes Intermsofpracticality pChartcan shouldbeusedwhensamplesizesareequalaspcarrymoremeaningthan ofrejectedunits np ComputingControlLimitsforpChart 31 Openthedatasetpchart jmp SelectControlChartfromtheGraphmenu Select DefectivesastheProcessvariable SelectLot astheSampleLabelvariable Verifyoptionsettings ChartTypeis IR IndividualMeasurementboxisselected MovingRangeboxisnotselected K sigmaisselected andK 3 RangeSpan 2 ClickonOK ExampleofComputingControlLimitsforpChart 32 Exercise2 ThedatasetExer2 jmpcontainsdefectlevelsforundissolvedflux Thenumberofunitsinspected thenumberofunitscontainingundissolvedfluxwererecordedoverseverallots MakeapChartforUndissolvedFlux Interpretthecontrolchart 33 InterpretationofpChart SomespecialcausesaffectingthepChart ChangesinvariabledataspecificationsChangesininspectionproceduresChangesintechnicianskills e g newtechniciansChangesinpiecepartsquality 34 Time relatedconditionwhereconsecutivedatavaluesarecorrelated i e dependent DatavaluescollectednearbyintimeareverysimilarDatavaluescollectedfarapartintimemaybeverydifferentTendtodriftovertime somedriftgradually othersmayhaveoccasionalsuddenchangesindirectionbetweenperiodsofrelativestability Autocorrelation 35 CautionWhenUsingMRMethod Ifthereisautocorrelation MR SummaryStat willunderestimatethetrueprocessvariation thecontrollimitswillbetoonarrowIfautocorrelationisevident useSigma StdDev Methodforcontrollimitscomputation RefertoAppendixB 36 ControlChartTrendRules Purpose ImprovetheresponsivenessofthecontrolchartDetectmoresubtleshiftsintheprocessmorequicklyDetectirregularitiesbeyondnormal3 thatindicatenon randomnessinprocess 37 HowtoInterpretaControlChart ItisbasedontheNormalDistribution 38 SPCTrendRules Rule 1 AsinglepointbeyondeithercontrollimitUses Detectsverylarge suddenshiftsFalsealarmrate 0 27 Example 39 SPCTrendRules Rule 2 9consecutivepointsonthesamesideofthecenterlineUses DetectssmallshiftsortrendsFalsealarmrate 0 39 Example 40 SPCTrendRules Rule 3 6consecutivepointssteadilyincreasingordecreasingUses DetectsstrongtrendsExample 41 SPCTrendRules Rule 4 14 ormore consecutivepointsarealternatingupanddown Uses Detectssystematiceffects suchasalternatingmachines operators suppliers etc Example 42 SPCTrendRules Rule 5 2outof3consecutivepointsatleast2stddevbeyondthecenterline onthesamesideUses DetectslargechangesFalsealarmrate 0 30 Example 43 SPCTrendRules Rule 6 4outof5consecutivepointsonthechartaremorethan1stddevawayfromtheCLUses Detectsmoderate sizedchangesFalsealarmrate 0 53 Example 44 SPCTrendRules Rule 7 15 ormore consecutivepointsarewithin1stddevoftheCLUses DetectsadecreaseinprocessvariationExample 45 SPCTrendRules Rule 8 8 ormore consecutivepointsareonbothsidesoftheCL butnonearewithin1stddevofit Uses DetectsanincreaseinprocessvariationExample 46 SelectionofTrendRules Usingalarge oftrendrulesisunwise sinceeachtrendrulehasafalsealarmrate thecumulativefalsealarmratecanbeverylargeFalsealarmrateisthefrequencyofcontrolchartsignalswhennothingatallisactuallywrongwiththeprocessFalsealarmsareundesirable Theyreduceproductivity increasecostsfromunnecessarilyshuttingdowntheprocessTheyerodeconfidenceincontrolchartsasusefultools Eventuallyallout of controlsignalsareignored Asaresult quality productivity costwillsuffer 47 TrendRuleRecommendations Allcontrolchartsshouldatleastusethe1strule Point UCLorPoint LCLForanautomatedSPCsystemwithautomatedapplicationofSPCtrendrules it shighlyrecommendedtoadd5thruletodetectlargeshiftsinmean i e 2outof3rule Addotherrulesdependinguponprocessknowledgeabilitytorespondcriticalityofthemonitorsensitivityrequirementsforthemonitor 48 TrendRuleRecommendations OnlyusethetrendrulesthatsignalprocessinstabilitiesforwhichyouarecapableofrespondingJustificationneededfornotusingotherSPCtrendrulesStddev rangechartsmaychoosenottoreacttoPoint LCL howeveraLCLonthesechartscanbevaluablefordetectingmetrologyproblemsorunexpectedprocessimprovement 49 TreatmentofOOCPoints EveryOOCpointsshouldhaveacompletedRFCwhereapplicable documentactionstakenDonecessaryadjustmentorcorrectiontotheequipmentorprocessasinstructedintheRFCwhereapplicable 50 TreatmentofOOCPoints ThecorrespondingequipmentshallbeshutdowniftheOOCsituationscannotbesolved non conformingpartsareproducedpercontrolchartRFCIfanyindividualdatavaluesfallsoutsidetheprocessspecificationlimits thendispositiontheaffectedmaterialpertherequirementsspecifiedintherespectiveprocessspecificationorputthematerialon holdforengineeringdisposition 51 WhentoReviseControlLimits Controllimitsshouldbereviewedperiodically monthlyorquarterly off linetoassessiftheyneedupdating Aminimumof30datapointsareneededbeforere calculatingcontrollimits Re computecontrollimitswhenasignificantprocesschangeisimplementedcurrentcontrollimitstoowideortoonarrow 52 ChangeRatio AchangeratiomaybeutilizedtodetectwhenthecurrentlimitsmaybeinappropriateLCLChangeRatio LCLcurrent LCLcalc srun run calc UCLChangeRatio UCLcalc UCLcurrent srun run calc AlargenegativechangeratiosuggeststighteningacontrollimitAlargepositivechangeratiosuggestswideningthecontrollimitNote srun run calc 2 66MR bar 3 53 GuidelinesforInterpretingChangeRatios Potentiallyaproblem ChangeRatio 1 0Definitelyaproblem ChangeRatio 1 5 GivenThickness jmpexample UCLcurrent 130 0LCLcurrent 70 0Newlycollecteddataresultedthefollowing UCLcalc 119 41LCLcalc 78 72srun run calc 2 66MR 3 20 35 3 6 78UCLChangeRatio UCLcalc UCLcurrent srun run calc 1 56LCLChangeRatio LCLcurrent LCLcalc srun run calc 1 28 Indicatesaneedtochangethecurrentcontrollimits ChangeRatioExample 55 ProcessCapability Processcapabilityistheabilityofaprocesstomeetspecifications Aprocessmustbestablebeforeitscapabilitycanbecomputed NotCapableCapableAcapabilityindexisastatisticthatquantifies describesthecapabilityofaprocess 56 SpecificationLimits Theregionwhereproductisknowntofunctionwellintermsofperformance yield reliability orotherdesiredoutcomeAcceptablerangeofvaluesforaproductparameterDefinewhatisacceptable unacceptableproductDeterminedbyDesignrequirements simulationmodelsEngineeringjudgement typicallyproducteng integration Customeragreement requirementsDatadrivenvalidation ProcesswindowcharacterizationHistoricaldataidentifyingin lineorEOLproblemsUsedtodetermineprocesscapability 57 ControlLimits Calculatedfromdata basedonactualprocessperformanceDescribethenaturalrangeofperformanceofastableprocessDescribetheamountofnaturalprocessvariationUsedtodetermineprocessstability 58 SpecLimitsvs ControlLimits SpecLimitsBasedonperformancerequiredoftheproductWhatthecustomerwants whatwewant Tellsuswhentodispositiontheproduct materialApplyonlytoindividual raw datavalues ControlLimitsBasedonactualhistoricalprocessperformanceWhattheprocessdelivers whatweget Tellsuswhentotakeactionontheprocess equipmentApplytosummarystatistics e g X bar stddev range etc charts Neverusespeclimitsonacontrolchart 59 Stabilityvs Capability Aprocessissaidtobeinstatisticalcontrolwhentheonlysourceofvariationisofnaturalcauses i e nospecialcausesvariationpresent AprocessissaidtobecapablewhenvariationfromnaturalcausesisreducedsuchthatitcanmeetproductspecificationtolerancewhenthecontrollimitsarewellwithinthespecificationlimitsAprocessissaidtobenotcapableifthecontrollimitsareoutsidethespecificationlimits 60 Exercise3 0 2 4 6 8 Interpretation