A multivariate control chart for simultaneously monitoring process mean and variability

Recently, monitoring the process mean and variability simultaneously for multivariate processes by using a single control chart has drawn some attention. However, due to the complexity of multivariate distribution, the existing methods in the univariate processes can not be readily extended to the multivariate processes. In this paper, we propose a new single control chart which integrates the exponentially weighted moving average (EWMA) procedure with the generalized likelihood ratio (GLR) test for jointly monitoring both the multivariate process mean and variability. Due to the powerful properties of the GLR test and EWMA, the new chart provides quite robust and satisfactory performance in various cases, including the detection of the decrease in variability and the individual observation at the sampling point, which are very important cases in many practical applications but may not be well handled by the existing approaches in the literature. The application of our proposed method is illustrated by a real data example in ambulatory monitoring.