Multivariate Bayesian control chart based on economic and economic-statistical design using Monte Carlo method and ABC algorithm

Recent studies on multivariate control charts are based on Hotelling's T2 control chart. Due to the fact that the Bayesian control charts in a univariate can be effective on performance of control charts, this paper has proposed the multivariate Bayesian control chart based on economic and economic-statistical design. As finding distribution of Bayesian statistic is too difficult, the Monte Carlo method has been employed in order to determine design optimum parameters (sample size, sampling interval and control limit). Also, artificial bee colony (ABC) algorithm has been applied to search for the optimal design parameters. Ultimately, the performance of the proposed control chart and Hotelling's T2 were compared for more in-depth investigation.