This study offers a comprehensive analysis of various multivariate control chart methods within the context of diverse data scenarios. It addresses both non-contaminated and contaminated settings in the Phase I. The research delves into the effectiveness of control limits established through bootstrap techniques to create robust control charts. Furthermore, it evaluates the performance of the newly proposed Projection Outlyingness (PO) \(T ^{2} \) control chart, making a comparison with the conventional Hotelling \(T ^{2} \) and Minimum Volume Ellipsoid (MVE) control charts. In cases where the data remains uncontaminated, our study demonstrates the superior performance of control limits obtained through the bootstrap method for robust control charts. This superiority is evident in the deviations of Average Run Length and Alarm Rate values from their nominal values. As contamination is introduced into the dataset, we observe a decline in the performance of the bootstrap method, particularly noticeable with higher contamination percentages. Simultaneously, our analysis of the PO control chart showcases its robustness and stability, particularly in scenarios involving data contamination and varying correlation structures within the covariance matrix. In comparison to classical and MVE control charts, the PO method consistently performs commendably. This research provides invaluable insights for practitioners seeking to implement effective quality control measures, highlighting the potential of the PO control chart as a reliable tool in real-world quality control applications, especially when data contamination and the high correlation structure of the covariance matrix is a concern.
