Reliability Modeling and Maintenance Optimization for Repairable Systems: A Stochastic Modeling and Learning-Based Approach.

Maintenance planning plays a critical role in ensuring the reliability, safety, and cost effectiveness of complex engineered systems across sectors such as aerospace, energy, and industrial infrastructure. These systems often operate under significant uncertainty arising from stochastic degradation processes, multiple failure modes, limited data availability, and constrained maintenance resources. As system complexity and performance expectations increase, there is a growing need for datadriven reliability models and maintenance optimization frameworks that can support robust and adaptive decision-making. The research presented in this dissertation develops reliability modeling and maintenance optimization approaches for engineered systems subject to stochastic degradation and operational uncertainty. From a data-driven perspective, the work combines statistical reliability analysis with reinforcement learning–based optimization to address maintenance decision problems where system behavior is only partially known and evolves over time. Trend Renewal Processes (TRP) are used to model non-stationary failure behavior and capture degradation trends in repairable systems, while average-reward reinforcement learning formulations are employed to optimize longrun maintenance policies under budgetary and operational constraints. The proposed methods are demonstrated through multiple real-world case studies, including reliability analysis of HVAC systems, vacuum circuit breakers with multiple failure modes, and maintenance scheduling applications motivated by NASA test infrastructure. The dissertation further examines the impact of modeling assumptions, parameter uncertainty, and policy design choices through sensitivity analyses and comparative studies between alternative learning and reliability formulations. Results show that the proposed frameworks improve reliability estimation accuracy, enable more effective preventive maintenance strategies, and support adaptive maintenance policies that outperform traditional rule-based approaches. Overall, this research contributes methodological advances in reliability modeling and maintenance optimization and provides practical insights for engineering decision-making in complex, data-limited environments.