Combinations of multivariate shewhart and MEWMA control charts for monitoring the mean vector and covariance matrix

When monitoring a process that has multivariate normal variables, the Shewhart-type control chart traditionally used for monitoring the process mean vector is effective for detecting large shifts, but for detecting small shifts, it is more effective to use the multivariate exponentially weighted moving average (MEWMA) control chart. It has been proposed that better overall performance in detecting small and large shifts in the mean can be obtained by using the MEWMA chart in combination with the Shewhart chart. Here we investigate the performance of this combination in the context of the more general problem of detecting changes in the mean or increases in variability. Recent investigations of combinations of the MEWMA chart for the mean and MEWMA-type charts based on the squared deviations of the observations from the target has shown that these combinations have excellent performance in detecting sustained shifts in the mean or in variability. Here we consider both sustained and transient shifts and show that a combination of two MEWMA charts has better overall performance than the combination of the MEWMA and Shewhart charts. We also consider a three-chart combination consisting of the MEWMA chart for the mean, an MEWMA-type chart of the squared deviations from target, and the Shewhart chart. When the sample size is n = 1, this three-chart combination does not seem to have better overall performance than the combination of the two MEWMA charts. When n > 1, the three-chart combination has significantly better performance for some mean shifts, but somewhat worse performance for shifts in variability.