Designing Bayesian paradigm-based CUSUM scheme for monitoring shape parameter of the Inverse Gaussian distribution

Bayesian Control charts have gained prominence as highly effective statistical instruments in overseeing manufacturing processes and ensuring adept management of process variability. The Bayesian methodology proves especially adept in managing uncertainties related to parameters within the manufacturing sector. In this research endeavor, our focus lies in establishing the threshold for monitoring the shape parameter of the Inverse Gaussian distribution (IGD) in phase-II based on cumulative sum (CUSUM) chart in classical and Bayesian frameworks using a variety of loss functions for enhancing their utility and applicability and have compared them with the Shewhart and EWMA control charts. We have also compared the proposed IGD-based CUSUM charts with the Lomax-based CUSUM charts. The evaluation of the proposed approach hinges on performance measures such as average run length (ARL), standard deviation of run length (SDRL), and median of run length (MDRL). Through simulation, the study showcases the efficiency of the Bayesian approach-based CUSUM charts, highlighting their superiority over the conventional classical setup-oriented CUSUM charts. Additionally, the proposed approach is employed in practical scenarios using real-data case studies from the aerospace manufacturing sector. The outcomes derived from real-data analysis substantiate and reinforce the conclusions drawn from the simulated results.