combined+schewhart-cusum+charts+with+variable+sampling+at+fixed+times

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1、torequirethatsamplesalwaysbetakenatspecifiedfixedtimes,withadditionalsamplesalowedbetweenthesefixedtimeswhennecessary.ThechartsusingthismodificationVSIideaarecaledvariablesamplingintervalwithsamplingatfixedtimes(VSIFT).Reynolds(1996b)showedthattheVSIFT了chartsprovidesalmostthesamedet

2、ectionabilityasthetraditionalVSIXcontrolscheme.StoumbosandReynolds(2001)extendthisideatothesequentialprobabilityratiotest.Recently,LinandChou(2005)extendstheideaofVSIFTXtotheothertwoadaptiveXcharts:thevariablesamplingratewithsamplingatfixedtimes(VSRFT)Xchartandthevariableparametersw

3、ithsamplingatfixedtimes(VPFT)了chart.How-~，therehasnotbeenanypaperconsideringtheVSIorVSSICUSUMchartswithsamplingatfixedtimes.ThusthispaperwouldextendtheideaofVISFTandVSSIFTtoCUSUMchartsandinadditiontothecombinedShewhart-CUSUMcharts.Inthispaper,combinedShewhart-CUSUMchartswhichalowfor

4、varyingthesamplesizeandsampleintervalareintroducedinthenextsection;TheVSIFTandVSRFTcombinedShewhart-CUSUMchartswhichareinclusivelycaledtheadaptivewithsamplingatfixedtimes(AFT)Shewhart-CUSUMchartsaredescribedinSection3;Theninsection4,acomparativestudyofTheFSI,VSIandAFTcombinedShewhar

5、t-CUSUMchartswillbeconductedandsomecond,i-ionswillbedrawnbasedonthestudy.Finaly,theMarkovchainmodelwhichareusedtoanalyzedtheperformanceofFTchartarepresentedintheAppendix互2TheVSIandVSSIShewhart-CUSUMChartsSupposethattheprocessofinteresthasaqualitycharacteristicXwhosedistri-butionisno

6、rmalwith、Aandstandarddeviationo.TheobjectiveistodetectanydeviationintheprocessmeanfromatargetvalueYo勿takingasequenceofsampleseachofsizenfromtheprocess,inwhichtheobservationswithinandbetweensamplesareassumedtobeindependent.'2.1DescriptionoftheVSIandVSSICombinedShewhart-CUSUMChartsFor

7、thejthsample(]=1,2,⋯)，considerthestandardizedstatistic易=而(不一po)/o,where兀isthesamplemean.Inpractice,itmaybenecessaryinmanycasestoestimatebothPoand。frompastdata,butforWea吕.sumethatuoandoareknown.ACUSUMschemeaccumulatesdeviationsofthesamplemeansthataremorethankstandardizedunitsfrompo.T

8、heparameterkisusual