Cumulative Sums Robustness and Resilience in the Context of Time Series Anomaly Detection

Abstract

Anomaly detection on time series data has been extensively studied for ensuring system reliability, process quality, and operational continuity across diverse domains such as engineering, manufacturing, and industrial monitoring. Detecting deviations from normal behavior can signal faults, degradations, or process drifts that may affect product quality or equipment reliability. Amid well‐known approaches, cumulative sums (CUSUMs) are widely used for their simplicity, low computational cost, and effectiveness in detecting gradual statistical changes. Over the years, many CUSUM variants have been proposed to identify changes in parameters such as the mean or variance. In practice, these methods are applied either directly to measured signals or to the prediction residuals of machine learning models. Despite their popularity, few studies have systematically evaluated their performance in terms of robustness, resilience, and computational efficiency under realistic noise and outlier conditions. This article presents a comprehensive analysis of six CUSUM approaches applied across four datasets and in both application modes. Robustness and resilience are assessed using three complementary metrics that quantify noise and outlier sensitivity, post‐anomaly recovery, and overall detection reliability. The results highlight the strengths and limitations of each method, offering practical guidance for deployment in quality and reliability monitoring systems. To ensure transparency and reproducibility, the complete framework and datasets are made publicly available.