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GLR control charts for monitoring the covariance matrix of bivariate normal processes
Journal of the Korean Data & Information Science Society 2018;29:1329-38
Published online September 30, 2018
© 2018 Korean Data and Information Science Society.

Jiayi Zhow1·Gyo-Young Cho2

12Department of Statistics, Kyungpook National University
Correspondence to: Professor, Department of Statistics, Kyungpook National University, Daegu, 702-701, Korea. E-mail: gycho@knu.ac.kr
Received August 20, 2018; Revised September 13, 2018; Accepted September 17, 2018.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
If we want to detect both small shifts and large shifts in means and variances, we use the generalized likelihood ratio (GLR) control chart, in which the range of shift sizes in the parameter does not need to be specifi ed, but can be estimated from the process data. There have been some works on developing GLR control charts speci fically for the problem of monitoring mean and variance. GLR control charts for monitoring the process mean of normal distribution were investigated. Also GLR control charts for monitoring the Bernoulli process were investigated. In the multivariate case, GLR control charts for monitoring the process mean vector of a bivariate normal distribution were investigated. In this paper, we will investigate the GLR control chart for monitoring the covariance matrix of bivariate normal process.
Keywords : Bivariate normal distribution, change point, covariance matrix, GLR control chart, SSATS.