Influence of process shifts in case of Six Sigma-based Bayesian control charts

Ravichandran Joghee and Ishah Maria Mathew

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 13, 4191-4206

Abstract: While traditional control charts play an important role in quality assurance activities, the work on such techniques evolved over the years particularly for early detection of process shifts. Many advanced level control charts have been proposed in the literature to even detect small shifts in the process as early as possible. In order to make use of the prior beliefs and likelihood of the observed data behavior, Bayesian control charts for parameter of the posterior distribution have been proposed by various authors. The Six Sigma-based control charts ensure smaller process variations by enforcing quality improvement activities and as a result, such processes would produce higher quality products with only 3.4 defects per million opportunities (DPMO) even after allowing a shift in the process up to ±1.5 times of process standard deviation. In this paper, an attempt has been made to develop Six Sigma-based Bayesian control charts. The proposed control charts incorporate various shift (or no-shift) combinations to prior and observed data behaviors to study their influence on the posterior parameter. Illustrative examples are also given for understanding the proposed approach. The performance evaluation and comparisons are also presented. The paper ends with a discussion and concluding remarks.

Date: 2025
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DOI: 10.1080/03610926.2024.2415383

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