On Monitoring of the Shape Parameter of the Inverse Gaussian Distribution via Memoryless Chart Under Bayesian Setup

The Inverse Gaussian distribution (IGD) is a probability distribution with several applications in various fields. The proposed study is prone to consider the problem of monitoring the shape parameter of IGD using the Bayesian method. The Bayesian setup effectively handles the situation in the manufacturing industry where parametric uncertainty is unavoidable. In this study, we focus on determining the monitoring threshold for the shape parameter of the IGD in phase-II and designing Shewhart control charts based on classical and Bayesian methods under different loss functions (LFs). The influence of hyperparameters on upper control limits (UCLs) has been explored. The evaluation is based on different performance measures such as average run length (ARL), the standard deviation of run length (SDRL), and the median of run length (MDRL). The simulation study illustrates the effectiveness of the proposed Bayesian Shewhart charts compared to the classical Shewhart chart. The suggested approach for Shewhart charts proves highly effective in promptly identifying shape parameter shifts and outperforming their classical counterpart in detecting faults quickly. Using a real dataset, the proposed technique is also exemplified, and the findings validate the conclusions based on simulative results.