Simulation studies for evaluating performance of bootstrap based robust T ² control chart in detecting highly outlier contaminated data

Hotelling's T² control chart is a multivariate control chart commonly used to monitor the mean process. An outlier can be defined as an observation that significantly deviates from other observations, which indicates that the observation is generated by a different process. Hotelling's T² control chart is unsuitable for detecting outliers, especially for highly outlier contaminated data. The performance of the T² chart in monitoring mean shifts can be increased if a robust estimator was utilized. Based on previous research, T² based on the Fast Minimum Covariance Determinant (Fast-MCD) estimator performs well in monitoring low to medium outlier contaminated data. Therefore, the Minimum Regularized Covariance Determinant (MRCD) estimator can be used to detect outliers in high dimensional data. On the other hand, this research focuses on developing a bootstrap based robust Hotelling's T² charts with Fast-MCD and MRCD estimators for evaluating performance in detecting highly outlier contaminated data. Based on the simulation, the proposed chart has an equal performance to robust T2 based on Fast-MCD when a small number of variables are applied. Moreover, using Area Under Curve (AUC) as a measure of goodness, the proposed chart successfully beat the conventional T² chart on all conditions and beat robust T² based on Fast-MCD on high dimension scenarios.