Multivariate Hierarchical Bayesian Control Charts for High-mix Low-Volume Production

Control charts are a typical method of statistical process control. They arose in the context of low-mix high-volume production. However, high-mix low-volume production has become mainstream as needs diversify, and parameter estimation accuracy has decreased because obtaining sufficient measurement values for each product is difficult. Therefore, performing process control using multivariate characteristics has become challenging. control chart is widely used for managing multivariate control characteristics and several multivariate control charts have emerged based on it, but these methods work only with a sufficient number of samples, more than in the univariate case. Therefore, conventional control charts are not applicable for low-volume production, research on Bayesian statistics-based control charts has been conducted and their usefulness has been demonstrated. Although previous studies have proposed control charts using hierarchical Bayesian modeling, these charts do not address multivariate data. Therefore, in this study, we propose multivariate hierarchical Bayesian control charts that can accommodate multivariate characteristics. By developing hierarchical Bayesian modeling that considers differences among product types, estimation accuracy can be improved even in high-mix low-volume production. According to the simulation analysis, the proposed method outperformed control chart in the high-mix low-volume production environment, and its performance also improved as the number of product types increased.