Robust Phase I monitoring of Poisson Regression Profiles in Multistage Processes

Document Type : CFP- Quality Engineering Techniques in Production and Service Systems


Department of Industrial Engineering, Faculty of Engineering, University of Torbat Heydrieh, Mashhad, Iran



The paper addresses the challenge of monitoring and controlling processes where the assumption of normality is violated, and the response variable follows a Poisson distribution instead. We also recognize the significant impact outliers can have on model estimators, which in turn affects the performance of control charts. To overcome these challenges, we propose the use of robust estimators for monitoring profiles and enhancing control chart efficiency. Furthermore, as industries increasingly adopt multistage processes in manufacturing instead of a single stage, monitoring these processes becomes essential. Therefore, our paper proposes two robust control charts, namely and control charts designed for Poisson regression profiles in multistage processes. We evaluate the efficiency of our proposed control chart using the signal probability criterion and compare its performance to that of a classic control chart in Phase I. We also conduct extensive simulation studies to appraise the performance of these control charts under different shifts and stages, considering contamination scenarios as well. Based on our simulation results, we find that the control chart based on robust estimators provides better performance compared to the classic control chart. This finding demonstrates the effectiveness of our proposed method. Additionally, we present a real example to further evaluate the performance of our approach.