In this article, a double-max multivariate exponentially weighted moving average (DM-MEWMA) chart is proposed to jointly monitor the parameters of a multivariate multistage auto-correlated (MMAP) process. While the process is assumed to work in a linear state-space form, two modified statistics are combined into a novel statistic to monitor the mean vector and the covariance matrix of the MMAP simultaneously. Besides, prior knowledge of variation propagation is used so that the chart has both a fault identification power and capability of working with the sample size of one. A statistical test shows that the two proposed statistics are independent of the process dimension. Monte Carlo simulation indicates that the DM-MEWMA chart has quite robust performance in detecting changes. Moreover, when the number of stages increases, it outperforms some existing alternative methods. In addition, fault identification comparison demonstrates that most of the moderate mean and variability shifts can be isolated by the DM-MEWMA chart. (C) 2015 Elsevier Ltd. All rights reserved.