An adaptive EWMA chart for Poisson process

This paper introduces an adaptive EWMA (AEWMA) chart designed for monitoring Poisson processes. This chart offers a streamlined implementation process, eliminating the need for additional parameters. Notably, it demonstrates the ability to effectively detect a range of the mean shift sizes. Using Monte Carlo simulations, this study provides estimates for various performance metrics, including the zero-state and steady-state average run-length (ARL), expected weighted run-length, and expected relative ARL profiles for existing and proposed charts. The results indicate that the AEWMA chart surpasses the performances of existing EWMA, CUSUM, and two other AEWMA charts in detecting multiple shifts in the process mean. Additionally, an illustrative example is presented to showcase the practical implementation of the considered charts.