Persistence-Based Absolute Relative Error for Alarm-Centric Monitoring Under Low-Frequency Manufacturing

Manufacturing condition monitoring in low-frequency sensing environments presents significant challenges for traditional anomaly detection methods, which depend on dense temporal observations or instantaneous thresholding. In these contexts, transient fluctuations often overshadow individual measurements, resulting in unstable and unreliable alarm responses. This paper addresses these challenges by framing anomaly monitoring as an alarm-centric decision problem specifically designed for low-frequency manufacturing sensor data. The proposed framework assesses deviations relative to stable idle-state reference values using absolute relative error (ARE), which provides a normalized and dimensionless representation of proportional degradation across diverse sensor features. Alarm decisions are then based on the persistence of threshold exceedances over consecutive idle-state observations, rather than relying on single-sample anomalies. By distinctly separating deviation modeling from alarm decision-making, the framework facilitates stable and interpretable alarm generation without depending on waveform reconstruction or parametric distribution assumptions. Validation of the framework is conducted using real industrial monitoring data under controlled fault-simulation conditions. The results indicate that persistence-based decision logic significantly enhances alarm reliability for both absolute and squared deviation baselines, while the ARE-based deviation yields superior discrimination for sustained proportional degradation. By combining ARE-based deviation modeling with persistence-based alarm decision logic, the proposed ARE-based persistence strategy achieves the highest reliability in alarm behavior among all methods compared, demonstrating its efficacy for low-frequency manufacturing monitoring.