Design of the One-Sided Run-Sum and EWMA Control Charts for Monitoring the Mean Shifts in Gamma-Distributed Processes

Abstract: Recognized for their simplicity and effectiveness, the run-sum (RS) and exponentially weighted moving average (EWMA) charts are frequently used for monitoring process mean shifts. Although these charts are commonly applied under the normal distribution, many practical manufacturing processes exhibit non-normal distribution. Therefore, this article introduces two one-sided RS and EWMA charts for non-normal processes, particularly the gamma process. Using the Markov chain approach, theoretical formulations of the run-length metrics, i.e., the average run length (ARL) and the expected ARL (EARL) under the gamma distribution are derived. Both zero-state and steady-state modes are examined. The optimal designs of the one-sided RS and EWMA charts by minimizing the out-of-control EARL for the unknown shift-size scenario are developed under the gamma distribution. This article also details the optimal charting parameters specific to gamma distribution. With the implementation of these new designs, our findings reveal that the proposed optimal one-sided RS and EWMA charts are effective and efficient in monitoring process mean shifts in gamma processes, outperforming other existing charts. Finally, the practicality and applicability of these proposed optimal charts are demonstrated using real-life manufacturing wafer process data.