An optimal joint predictive maintenance and mission abort policy under a cumulative working time success criterion

Mission-critical systems are subject to failures that not only result in mission revenue losses but also incur system failure penalties. Deciding on mission abort (AB) actions is crucial for maximizing profit. When a mission allows multiple attempts and its success is evaluated based on the cumulative execution time, maintenance can be implemented to increase the mission's success probability. This necessitates determining the system maintenance timing together with AB decisions, which is challenging due to the complex interactions between these two decision variables and the large state and action spaces. To date, designing an optimal joint predictive maintenance (PD) and AB policy for a system executing multiattempt missions under a cumulative execution time success criterion remains underexplored. This gap is filled in this study. Including the maintenance cost and allowing PD throughout the mission execution stage, we formulate the optimization problem as a Markov Decision Process with a continuous, state-heterogeneous action space. The structural properties of the optimal policy, including the continuity of PD actions with respect to the system state and control limits for AB, are derived. We leverage these properties to develop an improved value iteration algorithm. A case study of an unmanned aerial vehicle (UAV) demonstrates the proposed policy outperforms and is more robust than benchmark policies, and the proposed algorithm exhibits significantly higher computational efficiency than the standard method. Some counterintuitive results, such as noncontinuous maintenance decisions regarding the number of remaining attempts and the required remaining time to mission completion, are drawn.