Multivariate Bayesian control chart with estimated parameters

Abstract

In this paper, the effects of estimating the mean vector and covariance matrix on the performance of the multivariate Bayesian control chart are studied. Through using some indicative cases, we show that the economic performance is affected when the parameters are unknown compared to the known parameters case. We also show that when Mahalanobis distance (M-distance) is fixed, there are no significant differences between different shift directions. Furthermore, with the increase of the number of quality characteristics, the optimal expected average cost decreases in the case of estimated parameters. After investigating the sampling strategies of phase 2, we find the optimal expected average cost is significantly influenced by sampling interval and sample size. Finally, an example is given to show how to choose an enough the number of phase 1 samples.