Bayesian optimization of EWMA control charts: A case on process variance monitoring

Bayesian control charts (BCC) are gaining prominence as powerful statistical process control tools for analyzing manufacturing processes and managing process variability. This method is particularly useful for dealing with uncertain parameters in the manufacturing industry. This article introduces a novel Bayesian control chart (CC) framework that integrates a three-parameter logarithmic transformation with an exponentially weighted moving average (EWMA) approach to track process sample variance. The posterior estimates construct Bayesian EWMA charts for process variance under different priors. The newly designed Bayesian charts outperformed classical control charts in monitoring process variance. A simulation study reveals that the proposed Bayesian EWMA control charts outperform traditional classical EWMA charts in monitoring process variance. These advanced Bayesian charts demonstrate superior accuracy in detecting deviations in the variance of a normally distributed process and respond more quickly to shifts than conventional methods. Furthermore, the effectiveness of this approach is validated using real-world manufacturing data, with results aligning with the simulation findings, reinforcing the proposed technique's reliability.