Multivariate control charts for monitoring process mean vector of individual observations under regularized covariance estimation

Abstract

Multivariate control charts are generally used in industries for monitoring and diagnosing processes characterized by several process variables. The applications of charts assume that the in-control process parameters are known and the charts’ limits are obtained from the known parameters. The parameters are typically unknown in practice, and the charts’ limits are usually based on estimated parameters from some historical in-control datasets in the Phase I study. The performance of the charts for monitoring future observation depends on efficient estimates of the process parameters from the historical in-control process. When only a few historical observations are available, the performance of the charts based on the empirical estimates of the process mean vector and covariance matrix have been shown to deviate from the desired performance of the charts based on the true parameters. We investigate the performance of the multivariate Shewhart control charts based on several shrinkage estimates of the covariance matrix when only a few in-control observations are available to estimate the parameters. Simulation results show that the control charts based on the shrinkage estimators outperform the charts based on existing classical estimators. An example involving high-dimensional monitoring is provided to illustrate the performance of the proposed Shrinkage-based Shewhart chart.