GLR Control Charts for Monitoring Correlated Binary Processes
dc.contributor.author | Wang, Ning | en |
dc.contributor.committeechair | Reynolds, Marion R. Jr. | en |
dc.contributor.committeemember | Kim, Inyoung | en |
dc.contributor.committeemember | Woodall, William H. | en |
dc.contributor.committeemember | Jin, Ran | en |
dc.contributor.department | Statistics | en |
dc.date.accessioned | 2015-06-21T06:00:18Z | en |
dc.date.available | 2015-06-21T06:00:18Z | en |
dc.date.issued | 2013-12-27 | en |
dc.description.abstract | When 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.degree | Ph. D. | en |
dc.format.medium | ETD | en |
dc.identifier.other | vt_gsexam:2139 | en |
dc.identifier.uri | http://hdl.handle.net/10919/52981 | en |
dc.publisher | Virginia Tech | en |
dc.rights | In Copyright | en |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
dc.subject | Abrupt Change | en |
dc.subject | Average Time to Signal | en |
dc.subject | Change Point | en |
dc.subject | CUSUM Chart | en |
dc.subject | Generalized Likelihood Ratio | en |
dc.subject | Markov Chain | en |
dc.subject | Initial State | en |
dc.subject | Statistical Process Control | en |
dc.subject | Steady State. | en |
dc.title | GLR Control Charts for Monitoring Correlated Binary Processes | en |
dc.type | Dissertation | en |
thesis.degree.discipline | Statistics | en |
thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
thesis.degree.level | doctoral | en |
thesis.degree.name | Ph. D. | en |
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