Robust Rolling Hotelling Fault Detection for Stochastic Monitoring Under Transient Casewise Contamination

Hotelling’s T-squared statistic provides an interpretable framework for multivariate fault detection; however, its rolling implementation is highly sensitive to transient casewise outliers in the reference window. Such abnormal observations may inflate the sample covariance matrix, enlarge the monitoring boundary, and consequently mask subsequent moderate fault signals. This study proposes a robust rolling Hotelling fault detection method, denoted as RRH-FD, to reduce this masking effect. The proposed method estimates the rolling reference center and scatter matrix using reweighted minimum covariance determinant (RMCD) estimators, while each newly arriving observation is evaluated directly as a potential fault signal. The monitoring threshold is obtained using a robust Hotelling approximation rather than the classical Hotelling distribution. A simulation study was conducted under both clean and contaminated rolling reference scenarios. Under clean reference windows, the proposed robust procedures remained competitive with the classical rolling Hotelling detector, showing only a modest efficiency loss. Under contaminated reference windows, RRH-FD substantially improved detection performance. The adaptive RRH-FD method reduced the average detection delay by approximately 37.6% relative to the classical rolling detector, while the fixed MCD fraction 0.85 version achieved an approximate reduction of 42.4%. The proposed methods also improved early detection rates within the first 25 and 50 post-fault monitoring points. Boundary inflation was quantified using the log-determinant ratio between the classical sample covariance matrix and the RMCD scatter estimate. This analysis further confirmed that the advantage of RRH-FD becomes more pronounced as the classical covariance boundary is more strongly inflated by transient outliers. An R package, RRHFD, was developed to facilitate implementation and reproducibility.