A Robust Version of Hotelling's T2 Control Chart for Retrospective Location Analysis of Individuals Using BACON Estimators

Abstract

Hotelling's T2 chart is commonly used for Phase I analysis of individual multivariate normally distributed data. However, the presence of only a few outliers can significantly distort classical estimates of location and scale, thus rendering the resulting analysis ineffective. This poses a significant problem for the Hotelling's T2 chart practitioner because the desired output of a Phase I analysis is an outlier-free reference sample which can be used to estimate control limits for prospectively monitoring a process in Phase II. Careful selection of a robust parameter estimation method is therefore critical when the initial reference sample is suspected to contain multiple outliers. The purpose of this research is to propose a version of Hotelling's T2 chart that uses the blocked adaptive computationally efficient outlier nominators (BACON) algorithm to robustly estimate location and scale parameters in Phase I. The proposed control chart, which assumes individual multivariate normally distributed data with constant covariance, is designed to detect both individual outliers and sustained mean shifts. Using Monte Carlo simulation, the proposed method is compared to Hotelling's T2 chart using classical estimators as well as robust estimators such as the minimum volume ellipsoid (MVE), minimum covariance determinant (MCD), and clustering methods. Although the BACON-based version of Hotelling's T2 chart turned out to be less powerful than expected, it is significantly better than the classical approach and offers some improvement over existing robust methods at a fraction of the computational expense.