A Bayesian Approach to EWMA Control Charts for Enhanced Monitoring of Pareto‐Based Processes

ABSTRACT The Pareto distribution is widely applied in actuarial science, wealth distribution, finance, and other fields where data exhibits the behavior of 80% issues related with 20% reasons. Bayesian control charts (CCs) are increasingly recognized as one of the most efficient statistical tools for process monitoring that offer enhanced control over process variation by using prior knowledge of the process parameters distribution. Thus, Bayesian methodology is particularly effective for addressing parametric uncertainty in manufacturing processes when prior knowledge is available. Bayesian CCs offer a reliable substitute for Classical CCs by utilizing prior information. This article introduces a Bayesian Exponentially Weighted Moving Average (EWMA) CC designed for monitoring the shape parameter of Lifetime Pareto Distribution (LPD) processes. Here, we incorporating prior predictive approach and shape parameter is estimated. The posterior distribution of the shape parameter is derived and Bayesian estimates (BEs) are calculated. The performance of the proposed Bayesian EWMA CC is evaluated against the Classical EWMA chart, using performance metrics such as average run length (ARL) and Standard Deviation of Run Length (SDRL), obtained from Monte Carlo simulations. The results indicate that the Bayesian CC is more effective in handling parameter uncertainty and detecting small process shifts, across various shifts in the shape parameter and sample sizes. Additionally, prior data and expert opinion are utilized to extract the prior predictive distribution and elicit the hyper‐parameters. In practical applications, the hyper‐parameters are determined numerically, offering a comprehensive Bayesian framework for process monitoring. The practical utility of the Bayesian EWMA CC is demonstrated, with a particular emphasis on its flexibility in real‐world scenarios, such as monitoring survival time data in healthcare settings.