Interpretable anomaly detection framework using functional logistic regression

Sensor-driven anomaly detection is critical for yield and quality stability in semiconductor manufacturing. In real-world deployment, interpretability is increasingly necessary to determine which process variables drive anomalies and the timing of their occurrence. Multivariate process sensor time series are often noisy, incomplete, irregularly sampled, and high-dimensional, which complicates stable modeling and root-cause attribution. We propose an interpretable framework that smooths sensor traces with splines to form functional predictors, evaluates them on a common, feature-wise normalized time grid. Anomaly probabilities are then estimated using a variable-selecting functional logistic regression, which simultaneously identifies contributing sensors. To localize effects in time, we partition predictors and coefficient functions into predefined intervals to compute interval-wise contributions, yielding sensor-interval attributions. We demonstrate our method using some simulations with known anomaly sources and apply it to the D2 wafer-trace dataset (multivariate process sensor time series from semiconductor manufacturing) to identify contributing sensors and time intervals.

Anomaly detection

Semiconductor manufacturing

Interpretability

Multivariate sensor time series

Functional logistic regression

Interval-wise contribution 

Korean International Statistical Society