Multivariate control charts for monitoring the mean vector and covariance matrix

Multivariate control charts are considered for the simultaneous monitoring of the mean vector and covariance matrix when the joint distribution of process variables is multivariate normal. Emphasis is on the use of combinations of multivariate exponentially weighted moving average (MEWMA) control charts based on sample means and on the sum of the squared deviations from target. The performance of these combinations is compared with the performance of standard multivariate Shewhart charts and to combinations of univariate EWMA charts applied to each of the variables. The performance of these control charts with and without the use of Hawkins' (1991) method of regression adjustment of the variables is investigated. The performance of many of the control charts depends on the direction of the shift in the mean vector or covariance matrix, so performance is investigated for specific shift directions and also for averages over all directions. The best overall performance is achieved using a combination of MEWMA charts based on the sample means and on the sum of squared regression adjusted deviations from target.