CUSUMstyle

CUSUMstyle is a family of sequential monitoring methods inspired by the cumulative sum control chart (CUSUM). It provides a framework for detecting shifts in the central tendency of a process or signal by accumulating evidence over time and issuing alerts when this evidence crosses predefined thresholds. The approach emphasizes timely detection and interpretability, making it suitable for real-time decision making across diverse domains.

In its typical form, CUSUMstyle maintains a running statistic that aggregates deviations from a target baseline. A common one-sided version uses a baseline value mu0, a reference value k, and a decision threshold h. The cumulative sum is updated after each observation x_t, for example as S_t = max(0, S_{t-1} + (x_t - mu0) - k). An alarm is raised when S_t reaches or exceeds h. Two-sided variants track deviations in both directions, often by maintaining separate positive and negative sums. Variants may also incorporate weighting, adaptive baselines, or time-varying thresholds to cope with nonstationary data.

CUSUMstyle methods often feature online or incremental computation, enabling real-time detection with linear-time updates and low storage requirements. Extensions include adaptive estimation of mu0, k, and h, robust statistics to handle outliers, and integration with probabilistic or machine-learning models to improve performance in complex environments.

Applications span manufacturing quality control, cybersecurity (anomaly and intrusion detection), healthcare surveillance, environmental monitoring, and financial risk tracking. While offering fast detection and transparent decision rules, CUSUMstyle requires careful parameter tuning and validation, especially in nonstationary settings where baselines may drift or external factors influence observations.