A Multivariate Poisson Adaptive EWMA Control Chart

ABSTRACT The Multivariate Exponentially Weighted Moving Average (MEWMA) control chart is a highly recommended chart in the literature to monitor processes with the aim of detecting small and moderate process shifts. The MEWMA chart is designed to detect a predetermined shift size but not a range of different shift sizes simultaneously. An adaptive version of the MEWMA chart, namely, the Multivariate Adaptive EWMA (MAEWMA) chart, was introduced to provide the adaptability property to the chart based on the shift size the process currently experiences. However, the MAEWMA chart is rarely considered in the literature, especially with attribute characteristics. Our study aims to design and evaluate the performance of the Poisson MAEWMA (P‐MAEWMA) chart. We additionally conduct a performance comparison between the proposed chart and two competing charts, which are the Poisson MEWMA (P‐MEWMA) and Poisson Hotelling's T 2 (P‐ T 2 ) charts. Our simulation results show that the proposed P‐MAEWMA chart can achieve the best average run length (ARL) performance across the entire range of shifts, and thus it is recommended to be used for detecting shifts of various sizes. An illustrative example is also presented to show the superiority of the P‐MAEWMA chart in diminishing the inertia effect compared to the P‐MEWMA chart.