On the Monitoring of Inverse Gaussian Shape Parameter Using Bayesian CUSUM Charts Under Different Loss Criteria

ABSTRACT Bayesian control charts (BCCs) have gained prominence as effective tools for tracking manufacturing processes and managing variability with precision. Their strength lies in addressing parameter uncertainty, making them especially valuable in industrial applications. This research aims to define a monitoring boundary for the shape parameter of the Inverse Gaussian Distribution (IGD) and to construct several non‐informative Bayesian (NIB) cumulative sum (CUSUM) control charts, each incorporating a distinct loss function (LF). To evaluate their efficacy, both the proposed and existing charts are examined using a range of performance indicators. Through comprehensive simulation studies across various sample sizes, the performance of the new NIB CUSUM charts is thoroughly investigated. Results consistently show that these Bayesian‐based charts surpass traditional classical CUSUM charts in identifying changes in the shape parameter. The NIB charts offer improved fault detection accuracy and heightened responsiveness to process variations. To reinforce the simulation outcomes, the proposed approach is also tested on real manufacturing process data, confirming its practical applicability and effectiveness.