Robust Maximum Half-Normal Multivariate Control Chart Based on Det-MCD and Fast-MCD Estimators

Every company conducts evaluations to ensure the quality of its products and services, often utilizing multivariate simultaneous control charts to monitor the process mean and variability concurrently. The objective of this study is to overcome a significant limitation in the Maximum Half-Normal Multivariate Control Chart (Max-Half-Mchart): its vulnerability to outliers, which can trigger masking and swamping effects and lead to inaccurate process monitoring. The primary scientific contribution is the development of two robust versions of the Max-Half-Mchart by integrating the fast minimum covariance determinant (Fast-MCD) and deterministic minimum covariance determinant (Det-MCD) estimators into the chart’s statistical framework. The evaluation criteria for these methods include the average run length (ARL) to assess process shift detection speed and classification accuracy, false positive (FP) rate, false negative (FN) rate, and area under the curve (AUC) to measure outlier detection performance. Simulation results indicate that, while both robust charts effectively detect process shifts, the Det-MCD-based robust Max-Half-Mchart is particularly superior for lower contamination levels (5–20%), whereas the Fast-MCD-based chart performs best at higher contamination levels (30%). An illustrative application to ordinary Portland cement (OPC) quality data confirms the practical superiority of the Det-MCD approach, which detected six out-of-control signals compared with only two identified by conventional methods. These results suggest that the proposed robust charts are highly sensitive tools for maintaining quality in the presence of contaminated data.