A Multivariate Control Chart for Detecting Increases in Process Dispersion

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, Σ, is “larger” than that of the in-control process, Σ0, in the sense that Σ−Σ0 is positive semidefinite and Σ 6= Σ0. Assuming Σ0 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.