A robust control chart for monitoring count data with time-varying sample sizes

Count data are commonly used in the fields of public health surveillance, manufacturing, and safety monitoring. In practice, sample sizes of count data collected at different times often vary over time. Thus, statistical process control for count data with time-varying sample sizes is important and has received considerable attention in the literature. Most existing methods on this topic rely on parametric modeling, assuming a Poisson or negative binomial data distribution. However, such assumptions of the parametric methods are often invalid in practice, leading to unreliable performance of the associated control charts. Additionally, the mean of the process under monitoring is usually assumed to be constant over time, which does not hold in many applications, including disease surveillance where the disease incidence rate often displays a sinusoidal seasonal pattern. To address these issues, this paper develops a nonparametric exponentially weighted moving average control chart for monitoring count data with time-varying sample sizes, based on data categorization and categorical data modeling. Numerical studies show that this method can provide effective and robust process monitoring.