GLR Control Charts for Monitoring a Proportion

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dc.contributor.authorHuang, Wandien
dc.contributor.committeechairReynolds, Marion R. Jr.en
dc.contributor.committeememberWoodall, William H.en
dc.contributor.committeememberKim, Inyoungen
dc.contributor.committeememberDu, Pangen
dc.contributor.departmentStatisticsen
dc.date.accessioned2014-03-14T21:23:21Zen
dc.date.adate2011-12-19en
dc.date.available2014-03-14T21:23:21Zen
dc.date.issued2011-12-06en
dc.date.rdate2011-12-19en
dc.date.sdate2011-12-13en
dc.description.abstractThe generalized likelihood ratio (GLR) control charts are studied for monitoring a process proportion of defective or nonconforming items. The type of process change considered is an abrupt sustained increase in the process proportion, which implies deterioration of the process quality. The objective is to effectively detect a wide range of shift sizes. For the first part of this research, we assume samples are collected using rational subgrouping with sample size n>1, and the binomial GLR statistic is constructed based on a moving window of past sample statistics that follow a binomial distribution. Steady state performance is evaluated for the binomial GLR chart and the other widely used binomial charts. We find that in terms of the overall performance, the binomial GLR chart is at least as good as the other charts. In addition, since it has only two charting parameters that both can be easily obtained based on the approach we propose, less effort is required to design the binomial GLR chart for practical applications. The second part of this research develops a Bernoulli GLR chart to monitor processes based on the continuous inspection, in which case samples of size n=1 are observed. A constant upper bound is imposed on the estimate of the process shift, preventing the corresponding Bernoulli GLR statistic from being undefined. Performance comparisons between the Bernoulli GLR chart and the other charts show that the Bernoulli GLR chart has better overall performance than its competitors, especially for detecting small shifts.en
dc.description.degreePh. D.en
dc.identifier.otheretd-12132011-084926en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-12132011-084926/en
dc.identifier.urihttp://hdl.handle.net/10919/40405en
dc.publisherVirginia Techen
dc.relation.haspartHuang_W_D_2011.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectContinuous inspectionen
dc.subjectCUSUM charten
dc.subjectMoving windowen
dc.subjectShewhart charten
dc.subjectStatistical process controlen
dc.subjectSteady state average number of observations to sigen
dc.subjectSubgroupen
dc.titleGLR Control Charts for Monitoring a Proportionen
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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