Control Charts for Monitoring Correlated Poisson Counts with an Excessive Number of Zeros

The zero‐inflated Poisson distribution serves as an appropriate model when there is an excessive number of zeros in the data. This phenomenon frequently occurs in count data from high‐quality processes. Usually, it is assumed that these counts exhibit serial independence, while a more realistic assumption is the existence of an autocorrelation structure between them. In this work, we study control charts for monitoring correlated Poisson counts with an excessive number of zeros. Zero‐inflation in the process is captured via appropriate integer‐valued time series models. Extensive numerical results are provided regarding the performance of the considered charts in the detection of changes in the mean of the process as well as the effects of zero‐inflation on them. Finally, a real‐data practical application is given.