A Multivariate Control Chart Increases in Process Dispersion

• Activity Number: 475
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Quality and Productivity
• Author(s): Chia-Ling Yen*+ and Jyh-Jen Horng Shiau+
• Companies: National Chiao Tung University and National Chiao Tung University
• Keywords: Average run length ; Likelihood ratio test ; Multivariate process dispersion ; One-sided test ; Two-sided test

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 is "larger" than that of the in-control process. 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 chart are demonstrated through a semiconductor example.