Some principles for surveillance adopted for multivariate processes with a common change point

The surveillance of multivariate processes has received growing attention during the last decade. Several generalizations of well-known methods such as Shewhart, CUSUM and EWMA charts have been proposed. Many of these multivariate procedures are based on a univariate summarized statistic of the multivariate observations, usually the likelihood ratio statistic. In this paper we consider the surveillance of multivariate observation processes for a shift between two fully specified alternatives. The effect of the dimension reduction using likelihood ratio statistics are discussed in the context of sufficiency properties. Also, an example of the loss of efficiency when not using the univariate sufficient statistic is given. Furthermore, a likelihood ratio method, the LR method, for constructing surveillance procedures is suggested for multivariate surveillance situations. It is shown to produce univariate surveillance procedures based on the sufficient likelihood ratios. As the LR procedure has several optimality properties in the univariate, it is also used here as a benchmark for comparisons between multivariate surveillance procedures