A LASSO Chart for Monitoring the Covariance Matrix

Multivariate control charts are essential tools in multivariate statistical process control. In real applications, when a multivariate process shifts, it occurs in either location or scale. Several methods have been proposed recently to monitor the covariance matrix. Most of these methods use rational subgroups and are used to detect large shifts. In this paper, we propose a new accumulative method, based on penalized likelihood estimators, that uses individual observations and is useful to detect small and persistent shifts in a process when sparsity is present.