Using Runs Rules to Monitor an Attribute Chart for a Markov Process

摘要

Forsomerepetitiveproductionprocesses,thequalitymeasuretakenontheoutputisanattributevariable.Anattributevariableclassifieseachoutputitemintooneofacountablesetofcategories.Oneofthesimplestandmostcommonlyusedattributevariablesistheonethatclassifiesanitemaseither“conforming”or“nonconforming.”Atoolusedwithaconsiderableamountofsuccessinindustryformonitoringthequalityofaproductionprocessisthequalitycontrolchart.Inthispaper,asequenceofrandomvariables,Xi,i=1,2,…,isusedtoclassifyanitemasconformingornonconformingunderastationaryMarkovchainmodelandunder100%sequentialsampling.ThesequenceofrandomvariablestobeplottedonthecontrolchartisY,i=1,2,…,whereY1countsthenumberofconformingitemsbeforethefirstnonconformingitemandYi,i=2,3,.countsthenumberofconformingitemsbetweenthe(i-l)thandtheihnonconformingitems.Intheliterature,YiiscalledtheCRL(ConformingRunLength).Thecontributionofthispapertotheliteratureistopresentrunsrulesforanattributecontrolchartofthistype.Theefficiencyofthesechartsisevaluatedusingtheaveragerunlength(ARL)ofthecharts.ThesupplementalrunsrulesthatarepresentedaretwooutofthreevaluesofYi,i=1,2,…fallingbelowdeterminedlowerlimits,fouroutoffivevaluesofYi,i=1,2,…fallingbelowdeterminedlowerlimits,andeightoutofeightvaluesofYi,i=1,2,...fallingbelowdeterminedlowerlimits.