Enhancing operational decision-making in fault diagnosis for high-dimensional data streams with auxiliary information

Modern engineering systems, from advanced manufacturing processes to sophisticated electronic devices, generate high-dimensional data streams (HDS) that demand efficient operational strategies for quality management. While real-time anomaly detection is crucial, the importance of accurate post-signal fault diagnosis for root cause analysis has grown substantially. Current diagnostic methods often focus on isolated sequences of HDS, missing opportunities to leverage auxiliary information that can enhance decision-making. This paper introduces a novel framework to improve large-scale fault diagnosis in HDS environments, integrating auxiliary sequences within a multi-sequence multiple testing framework. Utilizing a Cartesian hidden Markov model, we develop a generalized local index of significance (GLIS) to assess the abnormality likelihood across data streams. Based on the GLIS, our proposed data-driven diagnostic procedure effectively harnesses auxiliary information, aiming to optimize operational decisions by minimizing the expected number of false positives in the primary sequence while maintaining control over the missed discovery rate. The asymptotic validity and optimality of this approach ensure its robustness in practical settings. We validate the efficacy of our method through comprehensive simulations and a real-world case study, demonstrating its potential to support more accurate and informed operational decisions.