Hierarchical Bayesian Control Charts Based on the Spatial Autoregressive Model

Abstract

This paper proposes hierarchical Bayesian control charts based on the spatial autoregressive model for trendy datasets in high-mix low-volume production. The control chart, which is a representative method of statistical process control, is plagued by sample shortages for each product type in high-mix low-volume production. In addition, during manufacturing processing equipment can deteriorate, which, in turn, can result in changing process averages, which, in turn, results in an increase in type I errors. Moreover, in high-mix, low-volume production, spatial dependence exists between different product types due to universal equipment being used. To address these problems, we design control charts that consider the spatial relationships among product types using hierarchical Bayesian modeling based on the spatial autoregressive model. To clarify the properties of the proposed method, we evaluate two production orders: completely random production orders and nonrandom production orders. The results suggest the proposed method is effective, especially in the case of a random production sequence and when there are large differences among product types.