Title: Multivariate Bayesian control chart with estimated parameters

Authors: Chao Tan; Jian Liu; Xing Zhang

Addresses: State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, Hunan, China ' State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, Hunan, China ' State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, Hunan, China

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.

Keywords: expected average cost; multivariate Bayesian control chart; parameters estimation; statistical process control; SPC.

DOI: 10.1504/IJISE.2017.085758

International Journal of Industrial and Systems Engineering, 2017 Vol.27 No.1, pp.107 - 121

Received: 10 Mar 2015
Accepted: 05 Sep 2015
Published online: 12 Aug 2017 *

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