DEVELOPMENT OF MULTIVARIATE CONTROL CHARTS FOR MONITORING HIGH-DIMENSIONAL PROCESSES.

Abstract

Multivariate control charts are generally used in industries for monitoring and diagnosing processes characterized by several process variables. In practice, many processes are characterized with enormous data that are correlated and have high-dimensional data. The applications of some existing multivariate control charts in Phase I assume that the in-control process or normal operating condition parameters are known, and the charts' limits are obtained from the known parameters. However, 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. This has led to the development of charts that are efficient for monitoring of high-dimensional processes when the parameters are unknown and only few historical observations are available. 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. In this research, Hotellings 2 T control charts are proposed for monitoring process variables characterized with enormous data that are correlated and high-dimensional in the presence of four different covariance structures. The performance of the proposed Hotellings 2 T control charts based on several shrinkage estimates of the covariance matrix when only a few in-control observations are available to estimate the parameters in high-dimensional processes in Phase I are investigated. Also examined in this research, is the performance of an autocorrelation induced weighted Hotellings 2 T control charts based on reduction methods for correlated high-dimensional nonlinear process. Simulation results show that the control charts based on the shrinkage and reduction methods outperform the conventional Hotellings 2 T control chart. Illustrative examples involving high-dimensional monitoring is presented to depict the performance of the developed monitoring schemes