Multivariate robust control charts for location and dispersion

Abstract

Statistical quality control plays a crucial role in maintaining process stability and product reliability across industrial and service sectors. However, the presence of outliers, data contamination, and high-dimensional measurements poses serious challenges to conventional monitoring methods. Classical control charts, though widely used, are highly sensitive to outlying observations, often leading to false alarms or missed detections of genuine process shifts. This research focuses on developing robust estimation and control chart methodologies for effective monitoring of bivariate and multivariate processes under such complex conditions. A major contribution of this study is the development of the Shrinkage Gnanadesikan- Kettenring (SGK) covariance estimator, a robust multivariate estimator derived from the Gnanadesikan–Kettenring approach. Simulation studies demonstrated that SGK efficiently identifies contaminated observations while maintaining low false detection rates across diverse data structures, including high-dimensional and low-sample-size cases. Comparative analysis with existing robust estimators such as Minimum Covariance Determinant (MCD), Robust Mahalanobis Distance-Shrinkage (RMD-S), Reweighted Orthogonalized Comedian (ROC), Sn, and Orthogonalized Gnanadesikan-Kettenring (OGK) established that SGK achieves superior robustness and computational efficiency. Building upon robust estimation, novel bivariate and multivariate control charts were developed for both individual observations and rational subgroups. These charts exhibited strong in-control performance comparable to classical Hotelling’s T² charts for clean data, while significantly outperforming them under contamination. Robust dispersion charts based on Sn Covariance, GK_Sn, GK_Qn, Comedian, ROC, and SGK within Multivariate Exponentially Weighted Mean Squared deviation (MEWMS) and Multivariate Exponentially Weighted Moving Variance (MEWMV) frameworks further enhanced detection of variability shifts with low false alarm rates. Real data applications validated the proposed charts’ effectiveness, robustness, and computational efficiency. This research contributes a unified framework for robust process monitoring, offering practical, scalable, and reliable tools for modern quality management. Numerical studies and real-world applications confirm the models’ capability to detect process shifts accurately, even under contamination and high dimensional conditions, ensuring enhanced decision making and operational reliability.