Enhancing Hotelling's <img src=image/12643156_01.gif> Control Charts with MADn Estimators for Robust Water Quality Monitoring

Statistical control charts are pivotal tools in monitoring Water Quality Index (WQI) processes, enabling timely assessment of whether a system is operating within acceptable control limits or experiencing deviations that may signal environmental risks. Classical univariate charts, although widely used, are inadequate for environmental datasets that contain multiple interrelated water quality parameters, thereby necessitating the use of multivariate control charts such as those based on Hotelling's <img src=image/12643156_02.gif> statistic. However, the classical Hotelling's <img src=image/12643156_02.gif> statistic is highly sensitive to outliers and violations of normality—conditions frequently encountered in water quality monitoring—which can diminish accuracy, stability, and anomaly detection capabilities. To address these limitations, this study proposes a robust variant of the Hotelling's <img src=image/12643156_02.gif> statistic that incorporates robust estimators of multivariate location and scatter, enhancing resilience to extreme values and non-normal data structures. Simulation studies demonstrate that the proposed method consistently maintains a nominal Type I error rate between 0.025 and 0.075, indicating strong statistical reliability. The methodology is further validated using real water quality datasets from the Juru River and the Kilang Ubi River, where the robust control chart identifies anomalies more promptly and reliably than classical methods. These results highlight the enhanced sensitivity, stability, and practical applicability of the robust Hotelling's <img src=image/12643156_02.gif> approach in environmental quality monitoring. The improved performance provides significant contributions to early-warning systems, pollution management strategies, and long-term river ecosystem protection. Despite its strengths, the method's computational demands and reliance on adequate sample sizes constitute notable limitations, suggesting avenues for future research in adaptive multivariate monitoring frameworks and hybrid robust strategies that can further improve water quality surveillance and decision-making.