Robust Bivariate Control Chart for Process Monitoring with Rational Subgroups

ABSTRACT This research focuses on the development of a robust bivariate control chart for monitoring processes in the presence of outliers, particularly for rational subgroups. Multivariate control charts, especially Hotelling's T 2 chart, are widely used to detect shifts in the process mean vector by utilizing historical data in Phase I and real‐time data in Phase II. However, traditional Hotelling's T 2 charts can be sensitive to outliers and non‐normal data, leading to inaccurate results. To address these limitations, this study proposes a robust alternative that employs the L 1 median vector and robust covariance estimators, including the Comedian estimator, S n covariance, and Gnanadesikan–Kettenring (GK) estimator. These estimators, chosen for their high breakdown points, are used to robustly estimate the process parameters in Phase I, allowing the control chart to perform well even under challenging conditions. The control limits are empirically determined via simulations, with the upper control limits provided for different sample sizes and alarm probabilities. The proposed control chart's performance is evaluated through simulations with various scenarios, analyzing its ability to detect process changes while minimizing false alarms. The procedure is further illustrated using a dataset, demonstrating the proposed chart's practical application and robustness.