Development of a Bayesian Re‐weighted Adaptive EWMA Control Chart with Variable Sampling

Abstract

This study introduces a Bayesian Variable Sample Size (VSS) Re‐weighted Adaptive Exponentially Weighted Moving Average (VRAEWMA) control chart that incorporates a sigmoid adjustment function for efficient detection of process mean shifts. By integrating Bayesian inference with the adaptive VRAEWMA framework, the proposed method dynamically adjusts the sample size according to the magnitude of detected process deviations. This adaptive mechanism improves sensitivity to small and moderate shifts while simultaneously optimizing resource utilization. Extensive simulation experiments demonstrate that the Bayesian VRAEWMA with VSS–sigmoid outperforms classical fixed‐sample EWMA and existing adaptive EWMA schemes (AEWMA‐I, AEWMA‐II, SAEWMA), particularly in terms of average run length (ARL) performance, reduced false alarms, and faster detection capability. The results confirm that the proposed chart provides a more robust, flexible, and cost‐effective solution for industrial process monitoring. To enhance practical relevance, the proposed framework can be applied to real‐world manufacturing environments where adaptive sampling is essential for balancing efficiency and accuracy. Future work may extend this approach to multivariate processes, non‐normal distributions, and advanced machine learning–based adjustment strategies. Overall, the Bayesian VRAEWMA and sigmoid adjustment establishes itself as a powerful adaptive tool for modern statistical process control.