统计过程控制之先进控制图培训英文

StatisticalProcessControl:

AdvancedControlChartCourseContentVariablesControlChartsX-MRChartCusumChartEWMAChartPre-ControlChartAttributesControlChartsCumulativeCountChartX-MRChartApplicationswheresamplesizeforprocessmonitoringisn=1100%automatedinspectionandmeasurementproductionrateisveryslowrepeatabilityofmeasurementisnegligiblevariationwithinunit(e.g.rollofpaper)isnegligibleTheX-MRChart(orI-MRChart)isausefulcontrolchartifthecharacteristicisindependentlyandnormallydistributed.X-MRChartIf Xiisthemeasurementobtainedduringsamplingi,thentheMovingRange

MRiisgivenby MRi=Abs{Xi-Xi-1}=|Xi-Xi-1|e.g. MR1=|X1-X0| MR2=|X2-X1| MR3=|X3-X2|X0maybesetatsomehistoricalestimateoftheprocessmean.IfX0isomitted,thenMR1isnotcalculated.ControlLimitsofXandMRchartsTheCenterLineandControlLimitsofaXChartareTheCenterLineandControlLimitsofaMRChartareExampleTheFPCpinpulloutforcetestisdestructivetest.Only1pcsamplingpershiftisallowed.Over50shiftsofFPCpinpulloutforceiscollectedandreviewedtodetermineiftheprocessisin-statisticalcontrol?SN Force1 34.782 35.293 33.384 36.545 38.526 39.327 38.378 37.179 35.3210 36.9811 37.0312 37.1513 37.6214 37.7615 38.6416 33.8017 34.0418 36.1619 38.7937.6821 37.5622 38.1323 36.5024 35.1725 38.7326 38.0827 36.6528 36.0029 36.6130 37.9631 39.2132 37.3533 35.1434 37.4535 35.2136 38.6937 34.8438 36.8039 36.5640 37.7141 35.3442 39.4643 38.4044 39.9145 34.4046 36.8347 35.1648 37.9649 37.4550 35.43ExampleMiniTab’sStatControlChartsI-MRExampleX-MRChartsThemovingrangesarecorrelated,i.e.theyaredependentonthecurrentandpreviousdatapoints(X0andXi-1).ThiscorrelationmayinduceapatternofrunsorcyclesontheMRChart.Avoidorignoresecondaryindicatorsofinstability.TheShewhartModelShewhartModel: Yt=+tThismodelisbasedonthefollowingassumptions:TheprocesscenterisconstantexceptforchangesduetoAssignablecausesAslongastheprocessisstable,thepointsonthecontrolchartarerandomandindependentsamplesfromthesamedistribution“Tweaking”theprocesswillresultinincreasedvariabilityTheRealWorldModelInmanyprocesses,especiallycontinuousprocesses,themeandriftsandconsecutivesamplestendtobecorrelated.Consequently,Themeanisnotfixed,butjumpsupwardordownwardormeandersaroundTheinherentprocessvariabilitytmaynotbeindependent“Tweaking”theprocessmaydecreasevariabilityNot“tweaking”theprocessmayincreasevariabilityOtherthanShewhartControlChartDespiteitsshortcomings,theShewhartChartcontinuestobethemostcommonlyemployedcontrolchartbyvirtueofitseaseinimplementationandinterpretation.However,theShewhartChartonlyusestheinformationabouttheprocesscontainedinthelastsampling.Hence,itisnotsensitiveindetectingsmallshiftsinprocessparameters.Twocontrolchartsareknowntobesensitiveindetectingsmallshiftsinparameters––theCUSUMChartandtheEWMAChart.CUSUMChartTheCUSUMChartusesthedatainacumulativeform,whichisusuallythesumofdeviationsfromatargetvalue.0=targetvalueXi=individualvalueorsubgroupaverageXi-0=deviationfromtarget(Xi-0) =CUSUM,sumofdeviationsfromtargetCUSUMisshortforcumulativesum.TypesofCUSUMChartTherearetwomethodsfordetectinganout-of-controlsituationonaCUSUMChart:V-MaskDecisionIntervalMethodMiniTabreferstothemasTwo-Sided(V-Mask)CUSUMOne-Sided(LCL,UCL)CUSUMOne-sidedCUSUMSchartThisCUSUMChartactuallygenerates2one-sidedCUSUMSanupper-sidedCUSUMfordetectingupwardshiftsintheleveloftheprocessalower-sidedCUSUMfordetectingdownwardshiftsintheleveloftheprocessThischartusesUpperControlLimitandLowerControlLimittodeterminewhenanout-of-controlsituationhasoccurred.DesigningOne-sidedCUSUMchartTodesignaOne-SidedCUSUMChartSelectthesmallestacceptablein-controlAverage-Run-LengthARL,whereDecideonthesmallestshiftinthemeanforwhichquickdetectionisimportant.SelectkthatproducestheminimumARLattheshiftselected.Commonly,Determineh(numberofstandarddeviationsbetweentheCenterLineandtheControlLimits)suchthatthechartproducesthedesiredARL.Refertographonfollowingpageforselectionofh.AnOptimalDesignofCUSUMQualityControlChartsbyGanFF,JournalofQualityTechnology(Vol23,No4,Oct1991),Source:ExampleThedataarethicknessmeasurementsforasputteredplatinumlayer.4wafersaremeasuredforeachshiftandthevaluesareaveragedandcomparedtoatargetvalueof250Ä.S/NXiXi-250(Xi-250)1 263.513.513.52 248.0-2.011.53 227.5-22.5-11.04 245.5-4.5-15.55 235.5-14.5-30.06 249.0-1.0-31.07 234.3-15.7-46.78 259.89.8-36.99 280.030.0-6.910 264.514.57.611 252.52.510.112 258.38.318.413 259.59.527.914 239.5-10.517.415 269.319.336.716 259.89.846.517 269.519.566.018 249.0-1.065.019 246.0-4.061.020 267.017.078.021 274.324.3102.322 265.015.0117.323 263.013.0130.324 255.05.0135.3ExampleDesignaOne-SidedCUSUMChartthatwouldhaveafalse-alarmonlyonceper300samplings,andbesensitivetoaprocessdriftof1.5standarddeviations.ARL=300k =½½(1.5)=0.75FromthehvskChartonpage17, h=3.2ExampleExampleExampleRedopreviousexampleusingMiniTab’’sdefaultsofh=4andk=0.5Note: 1)k=0.5= morestringentdriftsensitivity2)h=4andk=0.5ARL200 higherchanceofaType-IErrorExampleExampleShewhartvsCUSUMPre-ControlchartPre-Controlisaprocedureusedtodetectprocessshiftsorchangesinvariability,forcontrollingcharacteristicswithintheirtolerances.Conventionalcontrolchartsarebasedontheinherentvariabilityoftheprocess,andaredesignedtotodetectprocesschangesthatarestatisticallysignificant.Pre-Controlisbasedonthecapabilityoftheprocesstomeetspecificationlimits.Pre-ControlChartThePre-ControlChartcomprisesfivezones.TargetValueUpperSpecificationLimitLowerSpecificationLimitUpperPre-ControlLimitLowerPre-ControlLimitGreenZoneYellowZoneYellowZoneRedZoneRedZone