The Pearson Residual‐Based Control Charts for Monitoring Overdispersed Count Sequences

ABSTRACT Most existing control charts are designed for positively autocorrelated count data and seldom address the issue of overdispersion. The log‐linear Poisson autoregression model (LLPAM) can capture overdispersion in count data, accommodate both positive and negative autocorrelations, and incorporate real‐valued covariates. This makes it a more flexible alternative to the standard Poisson model. However, Shewhart‐type charts applied to LLPAM often exhibit inflated false alarm rates and reduced sensitivity to parameter shifts under moderate temporal dependence. To address these limitations, we propose two monitoring schemes based on Pearson residuals (PRs): a Shewhart‐type chart and an exponentially weighted moving average (EWMA) chart. Both methods allow simultaneous monitoring of LLPAM parameters under positive or negative autocorrelation. Simulation studies show that the proposed PR‐based charts consistently outperform the observation‐based Shewhart chart in terms of average run length (ARL), standard deviation of run length (SDRL), median run length (MDRL), and relative mean index (RMI), while maintaining false alarm rates close to nominal levels. An application to Escherichia coli infection data from North Rhine–Westphalia further demonstrates the practical utility of the proposed control charts.