Paper Title
Monitoring Covariance Matrix With Small Sample Size Through Eigenvalues

Abstract
Increasing attention has been devoted to the application of multivariate control charts in quality engineering. When a multivariate process shifts, it occurs in either the mean or the covariance matrix. Various methods have been proposed to monitor the covariance matrix through the matrix elements or the likelihood. Noted that the eigenvalues reflect the characteristics of a matrix due to the well-known relationship between the eigenvalues and the corresponding matrix. Thus, in this paper, we propose a new control chart for detecting the change of variability in multivariate processes through eigenvalues. The relationship between the eigenvalues and the process variability is captured effectively. Simulation results show that the proposed control chart gives a desirable performance under various scenarios when compared with existing control charts. Index terms- Covariance matrix, Eigenvalues, Control chart.