Optimizing Lognormal Process Monitoring With Bayesian Approach for Industrial Engineering Applications

ABSTRACT In this article, we introduce the Bayesian adaptive Max‐EWMA control chart designed to monitor both the mean and variance of processes following a lognormal distribution. By employing various loss functions, our Bayesian control chart demonstrates robust performance in detecting shifts in both the mean and dispersion across a wide range of magnitudes. We utilize Monte Carlo simulation techniques to compute run length characteristics, providing a thorough comparative analysis of the proposed chart against existing control charts in terms of run length performance. Our findings reveal the superior sensitivity of the Bayesian control chart to shifts of different magnitudes. To illustrate the practical applicability of our approach, we present a case study on the hard‐bake process in semiconductor manufacturing, showcasing its effectiveness when applying various loss functions. In conclusion, our research highlights the enhanced performance of the proposed Bayesian chart in detecting out‐of‐control signals.