Bayesian generalized likelihood ratio chart for Gaussian process variance with an application to monitoring hard-bake processes

Hongxing Cai, Amitava Mukherjee, Wei Yang and Jiujun Zhang

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 9, 2773-2790

Abstract: Nowadays, Bayesian methods have gained popularity among quality control researchers. Before this study, only KazemiNia, Sadeghpour Gildeh, and Abbasi Ganji (2021) proposed the Bayesian generalized likelihood ratio (BGLR) control chart to monitor the mean of a normal process. In this study, we proposed the BGLR control chart, the Bayesian cumulative sum (BCUSUM) control chart, and the combination of two Bayesian CUSUM (2BCUSUM) control charts to monitor the variance of a normal distribution process. The performance of these charts is evaluated in terms of the steady-state average time to signal. From the overall monitoring effect, with prior information known, the detection capability of the BCUSUM control chart is the best among the three control charts in terms of the results of the Monte Carlo simulation. Furthermore, an application of the proposed charts in monitoring the hard-bake process is discussed to illustrate its implementation design.

Date: 2025
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DOI: 10.1080/03610926.2024.2434941

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