Developing Bayesian Cumulative Quantity Control Charts for Monitoring Rayleigh Process

The mixture models are used in engineering processes to monitor the multiple‐cause defect systems. Most cumulative quantity control chart studies are based on simple and two‐component produce defect systems. According to the Bayesian framework, this paper proposes a cumulative quantity control chart for a three‐component mixture of Rayleigh distribution. The control structure of the suggested chart is designed, and its performance is judged using useful measures such as average run length (ARL), average length of inspection (ALI), and extra quadric loss function (EQL). Moreover, the Bayes estimators and posterior risk under various priors such as (uniform prior, Jeffery's prior, and square root gamma prior) by using symmetric and asymmetric loss functions such as the DeGroot loss function, precautionary loss function, and squared error loss function are also derived in this study. To highlight the practical aspects of the proposal, a case study is also provided.