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. / Ph. D.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/52981 |
| Date | 27 December 2013 |
| Creators | Wang, Ning |
| Contributors | Statistics, Reynolds, Marion R. Jr., Kim, Inyoung, Woodall, William H., Jin, Ran |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Dissertation |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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