A CUSUM Control Chart Based on Gamma-Poisson Distribution

Gamma-Poisson (GaPoi) distribution modeling is significant for monitoring the quality of production processes, particularly the number of nonconformities. We designed a cumulative sum control chart based on the GaPoi distribution (CUSUM-GaPoi) that demonstrated superior efficiency compared to existing charts for monitoring production processes. The run-length characteristics were analyzed using a Monte Carlo simulation approach to measure the performance of the CUSUM-GaPoi chart. The proposed chart revealed the process out-of-control earlier than existing charts. Finally, manufacturing industrial data from wafer processes were utilized to highlight the practical implications of the proposed chart, showing that it detects the number of product nonconformities earlier than existing charts.