Active Learning for Repairable Hardware Systems With Partial Coverage

Identifying the optimal diagnostic test and hardware system instance to infer reliability characteristics using field data is challenging, particularly when constrained by fixed budgets and minimal maintenance cycles. Active Learning (AL) has shown promise for parameter inference with limited data and budget constraints in machine learning and deep learning tasks. However, AL for reliability model parameter inference remains underexplored for repairable hardware systems. It requires specialized AL Acquisition Functions (AFs) that consider hardware aging and the fact that a hardware system consists of multiple subsystems that may undergo only partial testing during a given diagnostic test. To address these challenges, this paper proposes a relaxed Mixed Integer Semidefinite Program (MISDP) AL AF that incorporates Diagnostic Coverage (DC), Fisher Information Matrices (FIMs), and diagnostic testing budgets. Empirical simulation experiments are designed for two diagnostic testing scenarios: (1) partial tests of a hardware system with overlapping subsystem coverage, and (2) partial tests where one diagnostic test fully subsumes the subsystem coverage of another. The proposed approach is evaluated against the most widely used AL AF in the literature (entropy), as well as several intuitive AL AFs tailored for reliability model parameter inference. The proposed AF ranked best on average among the alternative AFs across over 4500 experimental configurations, with respect to the Area Under the Curve (AUC) of the Squared Hellinger Distance (SHD) and Mean Squared Error (MSE) curves, with statistical significance.