Monitoring multivariate process variability via eigenvalues

- A method based on eigenvalues is developed for monitoring changes in the covariance matrix.
- The proposed approach performs well, especially under shifts in both variance and covariance elements.
- It is simple to implement compared to the penalized likelihood ratio-type methods.

Various methods have been proposed to monitor changes in a process covariance matrix. In view that a covariance matrix can be fully defined by its eigenvalues and eigenvectors, this paper suggests monitoring the covariance matrix based on eigenvalues as another alternative. Although there are some recent discussions about the use of eigenvalues for hypothesis testing in multivariate analysis, the use of them for monitoring covariance matrix changes has been less studied in multivariate quality control. The simulation results show that the proposed method performs especially well under simultaneous shifts in both variance and correlation elements and competitively under shifts in variance or correlation elements only, compared to the existing approaches. This demonstrates a good property of the proposed method being able to provide a robust detection performance under a wide variety of scenarios. A real example is also provided to illustrate the implementation of the proposed method.