GLR Control Charts for Monitoring Correlated Binary Processes

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dc.contributor.authorWang, Ningen
dc.contributor.committeechairReynolds, Marion R. Jr.en
dc.contributor.committeememberKim, Inyoungen
dc.contributor.committeememberWoodall, William H.en
dc.contributor.committeememberJin, Ranen
dc.contributor.departmentStatisticsen
dc.date.accessioned2015-06-21T06:00:18Zen
dc.date.available2015-06-21T06:00:18Zen
dc.date.issued2013-12-27en
dc.description.abstractWhen monitoring a binary process proportion p, it is usually assumed that the binary observations are independent. However, it is very common that the observations are correlated with p being the correlation between two successive observations. The first part of this research investigates the problem of monitoring p when the binary observations follow a first-order two-state Markov chain model with p remaining unchanged. A Markov Binary GLR (MBGLR) chart with an upper bound on the estimate of p is proposed to monitor a continuous stream of autocorrelated binary observations treating each observation as a sample of size n=1. The MBGLR chart with a large upper bound has good overall performance over a wide range of shifts. The MBGLR chart is optimized using the extra number of defectives (END) over a range of upper bounds for the MLE of p. The numerical results show that the optimized MBGLR chart has a smaller END than the optimized Markov binary CUSUM. The second part of this research develops a CUSUM-pp chart and a GLR-pp chart to monitor p and p simultaneously. The CUSUM-pp with two tuning parameters is designed to detect shifts in p and p when the shifted values are known. We apply two CUSUM-pp charts as a chart combination to detect increases in p and increases or decreases in p. The GLR-pp chart with an upper bound on the estimate of p, and an upper bound and a lower bound on the estimate of p works well when the shifts are unknown. We find that the GLR-pp chart has better overall performance. The last part of this research investigates the problem of monitoring p with p remains at the target value when the correlated binary observations are aggregated into samples with n>1. We assume that samples are independent and there is correlation between the observations in a sample. We proposed some GLR and CUSUM charts to monitor p and the performance of the charts are compared. The simulation results show MBNGLR has overall better performance than the other charts.en
dc.description.degreePh. D.en
dc.format.mediumETDen
dc.identifier.othervt_gsexam:2139en
dc.identifier.urihttp://hdl.handle.net/10919/52981en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectAbrupt Changeen
dc.subjectAverage Time to Signalen
dc.subjectChange Pointen
dc.subjectCUSUM Charten
dc.subjectGeneralized Likelihood Ratioen
dc.subjectMarkov Chainen
dc.subjectInitial Stateen
dc.subjectStatistical Process Controlen
dc.subjectSteady State.en
dc.titleGLR Control Charts for Monitoring Correlated Binary Processesen
dc.typeDissertationen
thesis.degree.disciplineStatisticsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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