Calibrated Prediction Set in Fault Detection with Risk Guarantees via Significance Tests

Abstract

Fault detection is crucial for ensuring the safety and reliability of modern industrial systems. However, a significant scientific challenge is the lack of rigorous risk control and reliable uncertainty quantification in existing diagnostic models, particularly when facing complex scenarios such as distributional shifts. To address this issue, this paper proposes a novel fault detection method that integrates significance testing with the conformal prediction framework to provide formal risk guarantees. The method transforms fault detection into a hypothesis testing task by defining a nonconformity measure based on model residuals. It then leverages a calibration dataset to compute p-values for new samples, which are used to construct prediction sets mathematically guaranteed to contain the true label with a user-specified probability, $1-α$. Fault classification is subsequently performed by analyzing the intersection of the constructed prediction set with predefined normal and fault label sets. Experimental results on cross-domain fault diagnosis tasks validate the theoretical properties of our approach. The proposed method consistently achieves an empirical coverage rate at or above the nominal level ($1-α$), demonstrating robustness even when the underlying point-prediction models perform poorly. Furthermore, the results reveal a controllable trade-off between the user-defined risk level ($α$) and efficiency, where higher risk tolerance leads to smaller average prediction set sizes. This research contributes a theoretically grounded framework for fault detection that enables explicit risk control, enhancing the trustworthiness of diagnostic systems in safety-critical applications and advancing the field from simple point predictions to informative, uncertainty-aware outputs.