It has been shown in the literature that Bayesian control charts are optimal tools for statistical process control but very few results have been published in this area. For any control chart, three control chart parameters must be specified, namely the sample size, the sampling interval and the control limit. Recently, industrial practitioners and academic researchers have increasingly recognized the cost benefits obtained by applying economically designed control charts to quality control, equipment condition monitoring and maintenance decision making. In this paper, design of a multivariate Bayesian control chart for condition-based maintenance (CBM) applications is considered using the control limit policy structure and including an observable failure state. Optimization models for the economic and economic statistical design of the multivariate Bayesian control chart for a three-state CBM model are developed and comparison results show that the multivariate Bayesian control chart performs better than the recently developed CBM chi-square chart.
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Yin et al. (2010) studied this question.