# Control charts for monitoring correlation coefficients in variance-covariance matrix

• Chang, Duk-Joon (Department of Statistics, Changwon National University) ;
• Heo, Sun-Yeong (Department of Statistics, Changwon National University)
• Accepted : 2011.06.29
• Published : 2011.08.01

#### Abstract

Properties of multivariate Shewhart and CUSUM charts for monitoring variance-covariance matrix, specially focused on correlation coefficient components, are investigated. The performances of the proposed charts based on control statistic Lawley-Hotelling $V_i$ and likelihood ratio test (LRT) statistic $TV_i$ are evaluated in terms of average run length (ARL). For monitoring correlation coe cient components of dispersion matrix, we found that CUSUM chart based on $TV_i$ gives relatively better performances and is more preferable, and the charts based on $V_i$ perform badly and are not recommended.

#### Acknowledgement

Supported by : Changwon National University

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