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Multivariate GLR control charts for the mean vector and covariance matrix
Journal of the Korean Data & Information Science Society 2018;29:1687-96
Published online November 30, 2018
© 2018 Korean Data and Information Science Society.

Seong Rae Jo1 · Gyo-Young Cho2

12Department of Statistics, Kyungpook National University
Correspondence to: Professor, Department of Statistics, Kyungpook National University, Daegu, 702-701, Korea. E-mail:
Received October 23, 2018; Revised November 14, 2018; Accepted November 15, 2018.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
In statistical process control, we want to detect a change in the process accurately and quickly. The GLR (generalized likelihood ratio) control chart has problems with calculating test statistics. In modern times, however, advances in computing systems have enabled GLR chart test statistics calculation. In this paper, multivariate GLR charts were developed to nd changes in the mean vector and covariance matrix. Another problem with the multivariate GLR control chart is that the covariance matrix has various forms. In particular, in order to calculate test statistics on the GLR chart, we need to assume that the determinant of covariance matrix increases, and that these assumptions are often unsatisfactory. To solve this problem, this paper suggested giving the lower limit of the covariance matrix. We showed that the GLR control chart is e ective in detecting shifts in mean vector and covariance matrix. Especially, the GLR control chart is e ective in detecting a wide range of shifts and the GLR control chart does not require initial parameters.
Keywords : Change point, covariance matrix, GLR control chart, mean vector, multivariate normal distribution, SSATS.