MEWMA charts when parameters are estimated with applications in gene expression and bimetal thermostat monitoring

Abstract

Multivariate exponentially weighted moving average (MEWMA) control charts for individual monitoring require a priori knowledge of the in-control parameters. In practice, this assumption is not always tenable, and estimated parameters are generally obtained from an in-control reference sample of m preliminary observations (Phase I sample). Here, we compared the Phase II performance of MEWMA control charts using different methods for estimating the covariance matrix when the in-control covariance structure is unknown, and only a small Phase I sample (Formula presented.) is available. The performance of the MEWMA control charts varied among the methods. For simulated data with small m, the performance of MEWMA control charts using a shrinkage estimate of the covariance matrix was superior (in terms of run-length properties) to the alternative methods considered in this study. The improved performance of MEWMA control charts using the shrinkage estimate was also demonstrated via illustrative case studies of bimetal thermostat and gene expression applications; changes were detected earlier by the shrinkage-based MEWMA method.