Monitoring Covariance Matrix with Small Sample Size Through Eigenvalues
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
Index terms- Covariance matrix, Eigenvalues, Control chart.