A note on GLR charts for monitoring count processes

Abstract

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.