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. Simultaneous multivariate control charts are widely used to monitor shifts in the process mean and variability at the same time. One Shewhart-type simul-taneous multivariate chart is the Max-Half-Mchart, which can detect both small and large shifts in the mean and variability. However, outliers can distort the estimation of process parameters used to set control limits. In addition, outliers can cause two related problems, namely the masking effect and the swamping effect. Recent studies have highlighted the importance of cellwise outliers. Previous studies have shown that cellwise contamination can trigger outlier propagation. Therefore, casewise-based ro-bust estimators become less relevant under such conditions. CellMCD is a robust method for estimating location and covariance by integrating cellwise outlier detection into a single objective function. This study aims to develop a robust Max-Half-M chart based on cellMCD. Based on simulation studies under different correlation levels and contamination proportions, the proposed chart shows more stable performance than the conventional chart and the robust Fast-MCD–based version, as indicated by higher AUC values and lower FN rates. The ARL analysis also suggests that the cellMCD-based chart tends to detect small to moderate shifts faster. In the real-data application, the cellMCD-based chart successfully detects seven out-of-control signals, which is more than the comparison charts.