Run-length percentiles of multivariate Poisson control charts

Average run length (ARL) is used to evaluate the performance of control charts. When the process is in-control, the run-length distribution is close to a geometric distribution. Hence, the mean of run-length distribution is ARL. When the process is not in-control, the run-length distribution may deviate from a geometric distribution. The run-length distributions have been studied for univariate and multivariate control charts. However, the run-length distributions of multivariate attribution control charts are lacking. Hence, we will investigate the run-length distribution of multivariate Poisson control charts in this study. The percentiles of the run-length distribution provide more information about the performance of multivariate Poisson control charts.