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1、ANewBivariateControlChartforMonitoringtheMeanVectorandCovarianceMatrixSimultaneouslyZHAOYongmanSchoolofMechanicalandElectricalEngineering,ShiheziUniversity,Shihezi,ChinaAbstract:Anewbivariatesinglecontrolchartisproposedtosimultaneouslymonitortheprocessmeanvectorandtheprocesscovariancematr
2、ix.Thischart,calledCSDWchart,isbasedonthecumulativesumofthediagonalelementsofWishartdistributedmatrix.Throughouraveragerunlength(ARL)comparison,theresultsofthesimulationshowthatthenewchartoutperformsthejointT2and
3、S
4、chartsandtheMax-MEWMAchartwhen(l)therearechangesinboththemeanvectorandthec
5、ovariancematrix,(2)therearechangesinthecovariancematrixonly.Examplesarealsogiventoillustratethenewchartprocedure.Keywords:Controlchart;CSDW;thejointT2and
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7、charts;Max-MEWMA;Averagerunlength1IntroductionStatisticalprocesscontrol(SPC)isoneofthemosteffectiveapproachesforqualityimprovement.Ac
8、ontrolchartisoneofthemostimportanttoolsoftenusedtoobservewhetheraprocessisincontrolornot.Therearemanysituationswhereitisnecessarytomonitoraprocesswithmorethanonequalitycharacteristicssimultaneously.ManymultivariatecontrolchartshavebeenpresentedintheliteratureofqualitycontrolsinceHotelling
9、fl],beingthefirstone,providedthe?2statisticformonitoringthemeanvector
10、iioftheprocess・ThefirstmultivariatecontrolprocedureformonitoringthecovariancematrixLwasderivedfromthegeneralizedlikelihoodratiotest.Forthebivariateprocess,Alt[2]developedthegeneralizedvariancestatistic
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12、tocontrolthecov
13、ariancematrixL・JacksonandWiley[3]mentionedthatanymultivariatecontrolchartsshouldpossessfourimportantproperties,namely,theyshouldanswerthesequestions:(1)whethertheprocessisin-control,(2)whetherthespecifiedprobabilityofType・Ierrorhasbeenmaintained,(3)whethertherelationshipsbetweenthevariabl
14、eshavebeentakenintoaccount,and(4)whattheproblemisiftheprocessisoutofcontrol.Thesubstantialamountofresearchesinnon-sequentialmultivariatequalitycontrolchartscanbeclassifiedintofourbroadcategories,namely,(1)MultivariateShewhartCharts,(2)MultivariateCumulativeSum(MCUSU
