Title page for ETD etd-12132011-084926


Type of Document Dissertation
Author Huang, Wandi
Author's Email Address wdhuang@vt.edu
URN etd-12132011-084926
Title GLR Control Charts for Monitoring a Proportion
Degree PhD
Department Statistics
Advisory Committee
Advisor Name Title
Reynolds, Marion R. Jr. Committee Chair
Du, Pang Committee Member
Kim, Inyoung Committee Member
Woodall, William H. Committee Member
Keywords
  • Continuous inspection
  • CUSUM chart
  • Moving window
  • Shewhart chart
  • Statistical process control
  • Steady state average number of observations to sig
  • Subgroup
Date of Defense 2011-12-06
Availability restricted
Abstract
The 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.

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