Statistica Sinica 20 (2010), 1683-1707

A MULTIVARIATE CONTROL CHART FOR DETECTING

INCREASES IN PROCESS DISPERSION

Chia-Ling Yen and Jyh-Jen Horng Shiau

National Chiao Tung University

Abstract: For signalling alarms sooner when the dispersion of a multivariate process is ``increased'', a multivariate control chart for Phase II process monitoring is proposed as a supplementary tool to the usual monitoring schemes designed for detecting general changes in the covariance matrix. The proposed chart is constructed based on the one-sided likelihood ratio test (LRT) for testing the hypothesis that the covariance matrix of the quality characteristic vector of the current process, $\bm\Sigma$, is ``larger'' than that of the in-control process, $\bm\Sigma_0$, in the sense that $\bm\Sigma - \bm\Sigma_0$ is positive semidefinite and $\bm\Sigma \neq \bm\Sigma_0$. Assuming $\bm\Sigma_0$ is known, the LRT statistic is derived and then used to construct the control chart. A simulation study shows that the proposed control chart indeed outperforms three existing two-sided-test-based control charts under comparison in terms of the average run length. The applicability and effectiveness of the proposed control chart are demonstrated through a semiconductor example and two simulations.

Key words and phrases: Average run length, likelihood ratio test, multivariate process dispersion, one-sided test, two-sided test.