Hotelling’s t² control charts based on robust estimators

Abstract

Under the presence of multivariate outliers, in a Phase I analysis of historical set of data, the T² control chart based on the usual sample mean vector and sample variance covariance matrix performs poorly. Several alternative estimators have been proposed. Among them, estimators based on the minimum volume ellipsoid (MVE) and the minimum covariance determinant (MCD) are powerful in detecting a reasonable number of outliers. In this paper we propose a T² control chart using the biweight S estimators for the location and dispersion parameters when monitoring multivariate individual observations. Simulation studies show that this method outperforms the T²control chart based on MVE estimators for a small number of observations.