Statistical Risk Heads for Failure Warning Across Time-Series Forecasters

Accurate time-series forecasting does not by itself specify when to issue a useful failure warning. This decision requires distinguishing approaching failures from normal operation while balancing missed events and false alarms. We introduce a statistical risk-head framework that adapts frozen forecasting models to failure warning using training targets that increase as failure approaches and degradation indicators computed from information available at prediction time. We train the risk heads using labels based on time remaining before failure, with additional losses that suppress high scores during safe operation, match changes in the target curve, and discourage falling risk as failure approaches. Warning thresholds are selected using training or calibration data. We evaluate the framework with DLinear, PatchTST, iTransformer, TTM, and FlowState on tiny-N-CMAPSS, NASA Battery Aging, XJTU-SY, and FEMTO/PRONOSTIA. Our system warns before more failures than a standard binary risk head in all 20 model–dataset pairs and improves 57 of 60 comparisons of event recall, false positive rate, and precision. Averaged equally across the 20 pairs, event recall increases from 65.98% to 87.35%, precision from 45.63% to 70.91%, and false positive rate decreases from 9.43% to 1.80%. These findings support statistical risk adaptation as a practical way to improve failure warnings across heterogeneous forecasting models.