Robust Max-Half-Mchart Based on the Cellwise Minimum Covariance Determinant

One of the main tools in Statistical Process Control (SPC) for monitoring quality is the control chart. The Max-Half-Mchart is a Shewhart-type simultaneous multivariate control chart designed to detect shifts in both process mean and variability. However, outliers can distort the estimation of process parameters used to set control limits, leading to masking and swamping effects. Recent studies have highlighted the importance of cellwise contamination, which can reduce the effectiveness of casewise robust estimators. To overcome this limitation, this study develops a robust Max-Half-Mchart using the cellwise Minimum Covariance Determinant (cellMCD) estimator for location and covariance estimation. The proposed chart was evaluated through simulation studies, average run length analysis, and applications to synthetic and real OPC cement quality data. Simulation results under different correlation levels and contamination proportions show that the proposed chart provides more stable outlier detection performance than the conventional Max-Half-Mchart and the Fast-MCD-based Max-Half-Mchart, with better discrimination between normal and contaminated observations. The ARL analysis also indicates faster detection of small to moderate shifts. In the synthetic-data application, it achieved an Accuracy of 0.9899 and an AUC of 0.9939 under 20% contamination, and in the real-data application it detected seven out-of-control signals. Overall, the findings demonstrate that incorporating cellMCD into the Max-Half-Mchart provides a more robust and effective approach for multivariate process monitoring under cellwise contamination.