Multivariate synthetic control charts based on high breakdown point robust location estimators

Multivariate synthetic control charts enable simultaneous monitoring of multiple process variables, thereby mitigating the inflation of false alarm rates typically observed when using separate individual control charts. However, the traditional synthetic control chart based on mean, Cmean, fails to produce reliable parameter estimates when data are contaminated with outliers. Moreover, the estimates cannot be obtained in a high-dimensional setting. Thus, this study addressed the gap by constructing three new robust multivariate synthetic control charts, CMRCD, CWS, and CWP, using the Minimum Regularized Covariance Determinant (MRCD) and Winsorized Modified One-step M-estimator (WMOM). The control charts were evaluated through extensive simulation studies using R, covering dimensions p = 2, 10, and 15 and sample sizes n = 5, 10, 15, 25, 50, 100, 200, and 500. The performances were assessed using the false alarm rate (α) and probability of detection. To demonstrate the applicability to real-world conditions, the proposed control charts were applied to river water quality data from Kampung Medan, Selangor. The simulation results demonstrate that the new control charts significantly outperform the Cmean in both stability and shift detection. Specifically, while the Cmean fails to control the α under high contamination, the CMRCD remains stable within Bradley’s stringent criteria (within 0.045 to 0.055). In terms of the probability of detection, the CMRCD outperforms the Cmean, achieving a probability of at least 0.80 in 174 conditions, whereas the Cmean meets this criterion in only 63 conditions. Based on the confusion matrix, real data indicate that new control charts can be effectively implemented in water quality monitoring contexts. Overall, the findings indicate that the CMRCD, CWS, and CWP perform better than the Cmean in contaminated conditions. The CMRCD is identified as the most robust and efficient monitoring tool in high-dimensional cases when data are contaminated