Nonparametric monitoring of multiple count data

Process monitoring of multiple count data has recently received considerable attention in the statistical process control literature. Most existing methods on this topic are based on parametric modeling of the observed process data. However, the assumed parametric models are often invalid in practice, leading to unreliable performance of the related control charts. In this article, we first show the consequence of using a parametric control chart in cases where the underlying parametric distribution is invalid. Then, we thoroughly investigate the performance of some parametric and nonparametric control charts in monitoring multiple count data. Our numerical results show that nonparametric methods can provide a more reliable and effective process monitoring in such cases. A real-data example about the crime log of the University of Florida Police Department is used for illustrating the implementation of the related control charts.