Hotelling's T2 control chart with two adaptive sample

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1、QualQuant(2009)43:903912DOI10.1007/s11135-008-9167-xORIGINALPAPERHotellingsT2controlchartwithtwoadaptivesamplesizesAlirezaFaraz·M.B.MoghadamPublishedonline:6May2008©SpringerScience+BusinessMediaB.V.2008AbstractSomequalitycontrolschemeshavebeendevelopedwhenseveralrelated

2、qualitycharacteristicsaretobemonitored.ThefamiliarmultivariateprocessmonitoringandcontrolprocedureistheHotellingsT2controlchartformonitoringthemeanvectoroftheprocess.Itisadirectanalogoftheunivariateshewhartx¯chart.Asinthecaseofunivariate,theARLimprovementsareveryimporta

3、ntparticularlyforsmallprocessshifts.Inthispaper,westudytheT2controlchartwithtwo-stateadaptivesamplesize,whentheshiftintheprocessmeandoesnotoccuratthebeginningbutatsomerandomtimeinthefuture.Further,theoccurrencetimeoftheshiftisassumedtobeexponentiallydistributedrandomvar

4、iable.KeywordsHotellingsT2controlchart·Adjustedaveragetimetosignal(AATS)·Adaptivesamplesize1IntroductionNowadaysthereisgrowinginterestinmultivariatestatisticalqualitycontrol,i.e.thesimultaneouscontrolofseveralrelatedqualitycharacteristicsofaprocess,becausequalitycontrol

5、problemsinindustrymayinvolvemorethanasinglequality(avectorof)characteris-tics.Thishasformedthebasisofextensiveworkperformedinthefieldofmultivariatequalitycontrol.Shewhart,whoisfamousforthedevelopmentofthestatisticalcontrolchart(Shewhartcharts)firstrecognizedtheneedtoconsi

6、derqualitycontrolproblemsasmultivariateinchar-acter.Agreatdealofworkonmultivariatestatisticalcontrolprocedureswasperformedinthe1930sandinthe1940sbyHotelling(1947).Jackson(1985)mentionedinhispaperthatA.Faraz(B)IndustrialEngineeringDepartment,SchoolofEngineering,TarbiatMo

7、daresUniversity,P.O.Box14115179,Tehran,Irane-mail:alireza.faraz@modares.ac.ir;alireza.faraz@gmail.comM.B.MoghadamDepartmentofStatistics,FacultyofEconomic,AllamehTabatabaeeUniversity,Tehran,Iran123904A.Faraz,M.B.Moghadamthemultivariatetechniquesshouldpossethreeimportantp

8、roperties:(1)theyproduceasingleanswertothequestionthatwhethertheprocessisin-control,and(2)whetherthespecifiedty