A new Bayesian multivariate exponentially weighted moving average control chart for phase II monitoring of multivariate multiple linear profiles

Recently, statistical profile monitoring methods have become efficient tools for monitoring the quality of a product (or a production process) using control charts. The key idea is to describe the relationship between a response variable and a set of explanatory variables in the form of a statistical regression model, which called profile. Traditionally, those control charts are constructed with standard "frequentistic" regression models. Recently, it has been proposed to apply Bayesian regression models instead, and it has been empirically demonstrated that Bayesian regression models have the potential to perform significantly better. In this paper, we introduce a novel Bayesian multivariate exponentially weighted moving average control chart for monitoring multivariate multiple linear profiles in phase II. The key idea is to use the data from historical data sets to generate informative prior distributions for the regression models in phase II. The results of our empirical simulation studies show that the Bayesian multivariate multiple linear regression model is superior to its classical "frequentistic" counterpart in terms of the average run length. Our empirical findings are in agreement with findings reported in recently published articles. To shed more light onto the merit of the proposed Bayesian method, we carry out a sensitivity analysis, in which we investigate how the amount of phase I data influences the results. We also demonstrate the applicability and superiority of the proposed Bayesian method by a real-world application.