A note on GLR charts for monitoring count processes

Various generalized likelihood ratio (GLR) charts have been proposed to monitor count processes such as binomial, Bernoulli, Poisson, and multinomial processes. The advantages of GLR charts are that designing the chart is relatively easy, estimates of the process change‐point and shift size are avai...

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Bibliographic Details
Published in:Quality and reliability engineering international 2018-10, Vol.34 (6), p.1041-1044
Main Authors: Lee, Jaeheon, Woodall, William H.
Format: Article
Language:English
Subjects:
Charts
Control charts
count process
generalized likelihood ratio chart
Likelihood ratio
maximum likelihood estimator
Monitoring
Process parameters
Signal processing
statistical process control
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Summary:Various generalized likelihood ratio (GLR) charts have been proposed to monitor count processes such as binomial, Bernoulli, Poisson, and multinomial processes. The advantages of GLR charts are that designing the chart is relatively easy, estimates of the process change‐point and shift size are available for post‐signal diagnosis, and they are effective in detecting a wide range of shifts in the process parameter. However, for some special cases of the observations, such as observing all defective items or all non‐defective items, the GLR chart statistic for monitoring a count process has been said to be undefined. We show that the GLR chart statistic is always well defined.
ISSN:0748-8017
1099-1638
DOI:10.1002/qre.2306