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1、StatisticalProcessControl AdvancedControlChart 2 CourseContent VariablesControlChartsX MRChartCusumChartEWMAChartPre ControlChartAttributesControlChartsCumulativeCountChart 3 X MRChart Applicationswheresamplesizeforprocessmonitoringisn 1100 automatedinspectionandmeasurementproductionrateisveryslowre
2、peatabilityofmeasurementisnegligiblevariationwithinunit e g rollofpaper isnegligibleTheX MRChart orI MRChart isausefulcontrolchartifthecharacteristicisindependentlyandnormallydistributed 4 X MRChart IfXiisthemeasurementobtainedduringsamplingi thentheMovingRangeMRiisgivenbyMRi Abs Xi Xi 1 Xi Xi 1 e g
3、 MR1 X1 X0 MR2 X2 X1 MR3 X3 X2 X0maybesetatsomehistoricalestimateoftheprocessmean IfX0isomitted thenMR1isnotcalculated 5 ControlLimitsofXandMRcharts TheCenterLineandControlLimitsofaXChartareTheCenterLineandControlLimitsofaMRChartare 6 Example TheFPCpinpulloutforcetestisdestructivetest Only1pcsamplin
4、gpershiftisallowed Over50shiftsofFPCpinpulloutforceiscollectedandreviewedtodetermineiftheprocessisin statisticalcontrol SNForce134 78235 29333 38436 54538 52639 32738 37837 17935 321036 981137 031237 151337 621437 761538 641633 801734 041836 161938 7937 682137 562238 132336 502435 172538 73 2638 082
5、736 652836 002936 613037 963139 213237 353335 143437 453535 213638 693734 843836 803936 564037 714135 344239 464338 404439 914534 404636 834735 164837 964937 455035 43 7 Example MiniTab sStat ControlCharts I MR 8 Example 9 X MRCharts Themovingrangesarecorrelated i e theyaredependentonthecurrentandpr
6、eviousdatapoints X0andXi 1 ThiscorrelationmayinduceapatternofrunsorcyclesontheMRChart Avoidorignoresecondaryindicatorsofinstability 10 TheShewhartModel ShewhartModel Yt tThismodelisbasedonthefollowingassumptions TheprocesscenterisconstantexceptforchangesduetoAssignablecausesAslongastheprocessisstabl
7、e thepointsonthecontrolchartarerandomandindependentsamplesfromthesamedistribution Tweaking theprocesswillresultinincreasedvariability 11 TheRealWorldModel Inmanyprocesses especiallycontinuousprocesses themeandriftsandconsecutivesamplestendtobecorrelated Consequently Themeanisnotfixed butjumpsupwardo
8、rdownwardormeandersaroundTheinherentprocessvariability tmaynotbeindependent Tweaking theprocessmaydecreasevariabilityNot tweaking theprocessmayincreasevariability 12 OtherthanShewhartControlChart Despiteitsshortcomings theShewhartChartcontinuestobethemostcommonlyemployedcontrolchartbyvirtueofitsease
9、inimplementationandinterpretation However theShewhartChartonlyusestheinformationabouttheprocesscontainedinthelastsampling Hence itisnotsensitiveindetectingsmallshiftsinprocessparameters Twocontrolchartsareknowntobesensitiveindetectingsmallshiftsinparameters theCUSUMChartandtheEWMAChart 13 CUSUMChart
10、 TheCUSUMChartusesthedatainacumulativeform whichisusuallythesumofdeviationsfromatargetvalue 0 targetvalueXi individualvalueorsubgroupaverageXi 0 deviationfromtarget Xi 0 CUSUM sumofdeviationsfromtargetCUSUMisshortforcumulativesum 14 TypesofCUSUMChart Therearetwomethodsfordetectinganout of controlsit
11、uationonaCUSUMChart V MaskDecisionIntervalMethodMiniTabreferstothemasTwo Sided V Mask CUSUMOne Sided LCL UCL CUSUM 15 One sidedCUSUMSchart ThisCUSUMChartactuallygenerates2one sidedCUSUMSanupper sidedCUSUMfordetectingupwardshiftsintheleveloftheprocessalower sidedCUSUMfordetectingdownwardshiftsinthele
12、veloftheprocessThischartusesUpperControlLimitandLowerControlLimittodeterminewhenanout of controlsituationhasoccurred 16 DesigningOne sidedCUSUMchart TodesignaOne SidedCUSUMChartSelectthesmallestacceptablein controlAverage Run LengthARL whereDecideonthesmallestshift inthemeanforwhichquickdetectionisi
13、mportant SelectkthatproducestheminimumARLattheshiftselected Commonly Determineh numberofstandarddeviationsbetweentheCenterLineandtheControlLimits suchthatthechartproducesthedesiredARL Refertographonfollowingpageforselectionofh 17 18 Example Thedataarethicknessmeasurementsforasputteredplatinumlayer 4
14、wafersaremeasuredforeachshiftandthevaluesareaveragedandcomparedtoatargetvalueof250 S NXiXi 250 Xi 250 1263 513 513 52248 0 2 011 53227 5 22 5 11 04245 5 4 5 15 55235 5 14 5 30 06249 0 1 0 31 07234 3 15 7 46 78259 89 8 36 99280 030 0 6 910264 514 57 611252 52 510 112258 38 318 413259 59 527 914239 5
15、10 517 415269 319 336 716259 89 846 517269 519 566 018249 0 1 065 019246 0 4 061 020267 017 078 021274 324 3102 322265 015 0117 323263 013 0130 324255 05 0135 3 19 Example DesignaOne SidedCUSUMChartthatwouldhaveafalse alarmonlyonceper300samplings andbesensitivetoaprocessdriftof1 5standarddeviations
16、ARL 300k 1 5 0 75FromthehvskChartonpage17 h 3 2 20 Example 21 Example 22 Example RedopreviousexampleusingMiniTab sdefaultsofh 4andk 0 5Note 1 k 0 5 morestringentdriftsensitivity2 h 4andk 0 5 ARL 200 higherchanceofaType IError 23 Example 24 Example 25 ShewhartvsCUSUM 26 Pre Controlchart Pre Controlisaprocedureusedtodetectprocessshiftsorchangesinvariability forcontrollingcharacteristicswithintheirtolerances Conventionalcontrolchartsarebasedontheinherentvariabilityoftheprocess andaredesignedtotodet
