A CUSUM control chart for the Gamma distribution with cautious parameter learning

In scenarios involving cycle times and processes governed by single specification limits, the Gamma distribution is a model that often characterizes the behavior of the data. While CUSUM control charts can achieve optimal performance in detecting shifts when in-control parameters are known, in practice, estimating Gamma parameters from limited Phase I samples can lead to an undesirable Phase II performance, as measured by the average run length (ARL). Approaches guaranteeing performance solve this issue at the expense of power. To address this challenge, our study introduces a CUSUM control chart for the Gamma distribution with cautious parameter learning. Using Monte Carlo simulations, we assess the ARL of a CUSUM scheme designed to monitor scale changes with estimated parameters. We demonstrate the efficacy of ARL performance with cautious learning, comparing performance under in-control and out-of-control conditions and emphasizing the guaranteed conditional in-control performance of our cautious learning approach. Finally, we demonstrate the practical applicability of this methodology in a packaging process using multi-head weighing machines. This research provides professionals interested in reliable monitoring schemes with implementation guidelines, including algorithms and reference tables.