Robust Multivariate Simultaneous Control Chart Based on Minimum Regularized Covariance Determinant (MRCD)

Control charts are widely used in the industrial world to monitor the average and variability of production processes. Max-Half-Mchart is a multivariate control chart that is not particularly effective in handling many outliers. This research aims to develop a control chart that is more resistant to outliers by using Minimum Regularized Covariance Determinant (MRCD). MRCD is a development of the MCD method, which is better at dealing with ‘fat data,” namely, situations in which the number of variables is greater than the number of observations. The performance of a robust Max-Half-Mchart control chart based on MRCD was evaluated using the average run length (ARL) against shifts in the process mean, process variance, and simultaneous shifts. A comparison was also made of the outlier detection accuracy between the robust Max-Half-Mchart based on MRCD and the standard Max-Half-Mchart. Simulation results demonstrated that the MRCD-based robust chart is most sensitive to simultaneous shifts in the mean and variance, significantly outperforming the conventional method in “de-masking” process deviations. The robust framework maintains higher accuracy and AUC levels even at extreme contamination stages of 30% to 40% outliers, where traditional charts typically fail. A practical application to cement quality data further substantiated these findings, as the robust chart successfully identified 14 out-of-control signals (comprising the mean, variability, and simultaneous shifts), whereas the conventional chart detected none. These results indicate that the MRCD-based Max-Half-Mchart offers a more reliable and responsive quality monitoring system for complex industrial datasets.