Title: Monitoring variability of multivariate processes

Authors: Amitava Mitra; Mark Clark

Addresses: Department of Aviation and Supply Chain Management, Raymond J. Harbert College of Business, Auburn University, Auburn, AL 36849-5266, USA ' Department of Aviation and Supply Chain Management, Auburn Technical Assistance Center, Raymond J. Harbert College of Business, Auburn University, Auburn, AL 36849-5266, USA

Abstract: The paper focuses on determining changes in process variability of multivariate processes. The problem is compounded by the fact that any of the elements in the variance-covariance matrix of variables could change, leading to a change in the process variability. While it may not be feasible to maintain individual control charts for each element of the variance-covariance matrix, some aggregate measure of the variability criteria could be monitored to initially determine if a change has occurred in the process variability. A couple of aggregate measures are proposed and the performance of these suggested measures is explored through a simulation procedure. Compared to the traditional method, which monitors the determinant of the variance-covariance matrix, these alternatives perform well. The performance measure used is the mean time to first detection of a change in the process variability.

Keywords: multivariate processes; process monitoring; process control; process variability; variance-covariance matrix determinants; generalised measure of variance; eigenvalue; eigenvector; matrix decomposition; simulation; out-of-control ARL; average run length; time to first detection.

DOI: 10.1504/IJQET.2014.060431

International Journal of Quality Engineering and Technology, 2014 Vol.4 No.2, pp.112 - 132

Published online: 14 Apr 2014 *

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