A study of multivariate (X̄, S) simultaneous control chart based on Kullback-Leibler information

Recently, the rapid growth of data-acquisition technology and the use of online computers for process monitoring have led to an increased interest in the simultaneous surveillance of several related quality characteristics or process variables. In general, related quality characteristics are assumed to be distributed as multivariate normal random variables. As a result, the multivariate control chart for the mean vector has been studied extensively in many works. Popularly, in the case that the quality characteristics are distributed as univariate normal random variables, the mean and variance are simultaneously treated as the objectives of surveillance. From this point, in the case that the quality characteristics are distributed as multivariate normal random variables, the mean vector and variance-covariance matrix should be simultaneously treated as the objectives of surveillance. Kanagawa et al. have proposed a (x̄, s) simultaneous control chart that enables the user to monitor both changes in the mean and variance in a process simultaneously based on Kullback-Leibler information when the quality characteristics are distributed as univariate normal random variables. In this study, as an extension of the (x̄, s) simultaneous control chart, we propose a multivariate (X̄, S) simultaneous control chart that enables the user to monitor both changes in the mean vector and variance-covariance matrix simultaneously. Further, the evaluation of the power for the proposed multivariate (X̄, S) simultaneous control chart is also considered.