New Optimization Framework Enhances Fleet Maintenance Under Operational Uncertainty

Industrial and defense operators managing complex fleets of mission-oriented systems face the continuous challenge of preparing multi-component assets for rigorous deployments during strictly limited maintenance breaks. In an investigation published in the journal Autonomous Intelligent Systems, researchers Ryan O’Neil, Abdelhakim Khatab, and Claver Diallo developed an integrated mathematical optimization framework that coordinates fleet selective maintenance, repair crew scheduling, and system-to-mission assignments under operational uncertainty. Engineered systems such as military aircraft, autonomous mobile robots, long-distance haulage trucks, and power plant infrastructure function through alternating sequences of operational missions and recovery intervals. Achieving the necessary probability of mission success requires carrying out targeted restorative actions during scheduled pauses. However, real-world fleet maintenance operations must operate within severe practical boundaries, including finite repairperson availability, strict budgetary limits, stochastic task completion durations, and unexpected variations in intermission lengths caused by shifting operational schedules.

Traditional formulations of the selective maintenance problem, originating from early enumeration models, focus on identifying the optimal subset of components and maintenance actions to perform on a single asset to maximize system reliability or minimize overall intervention costs. Subsequent research progressively extended these methods to complex configurations, multi-state systems, component dependencies, and stochastic task windows. Despite these advancements, classical fleet selective maintenance formulations consistently relied on several restrictive assumptions that fail to reflect complex industrial operations. Previous models generally presumed that upcoming missions were identical, demanding a uniform functional system configuration across all tasks, and assumed that every scheduled mission had to be completed. Furthermore, earlier frameworks typically treated maintenance task durations and break windows as fixed deterministic values, ignoring the inherent stochasticity introduced by unpredictable operating environments, varying repair technician experience levels, and unforeseen operational alerts that can suddenly truncate available break times.

To overcome these limitations, the research team structured a comprehensive decision-making model that simultaneously resolves four fundamental operational choices: the assignment of specific systems to distinct mission categories, the selection of exact components within each system requiring intervention, the determination of the appropriate maintenance level for each chosen component, and the optimal allocation of specific maintenance tasks among available repairpersons. The primary objective function minimizes the grand total cost, which balances the severe financial or operational penalties incurred from unselected missions against the direct variable costs of technician labor hours and the fixed overhead costs of hiring and deploying repair personnel. In real operational settings, resource scarcity often prevents technicians from servicing every degraded subsystem, making mathematical mission prioritization an essential requirement. If a particular asset cannot be restored to the precise reliability threshold demanded by a planned deployment, the framework dynamically reallocates resources or leaves missions unassigned, ensuring that active operations only deploy hardware verified to meet rigorous safety and readiness standards.

A core innovation of the proposed model is its accommodation of flexible system configurations tailored across multiple distinct mission types, each defined by unique operational durations, reliability thresholds, minimal fleet sizing requirements, and non-completion penalties. For instance, in an operational military aviation fleet, a logistics transport mission does not require the activation or servicing of combat weapon systems, whereas an offensive tactical sortie mandates fully operational targeting and munitions equipment. Each mission type is formally characterized by a parameter profile specifying the minimum count of ready systems needed to initiate the mission, the exact subset of required subsystems, the mission operating duration, and the required subsystem reliability threshold. If a system is assigned to a specific mission profile, every required subsystem must independently surpass the designated minimum reliability benchmark. This structural flexibility allows maintenance planners to avoid wasting valuable maintenance labor on non-essential equipment, directing scarce technician time strictly toward the mission-critical subsystems necessary for each impending flight or deployment.

Addressing the practical physical realities of modern industrial assets, the researchers developed a hybrid reliability assessment methodology that accounts for two distinct component classifications within multi-component systems: standard components and sensor-monitored critical components. In modern engineering contexts, equipping every individual part with advanced telemetry sensors is economically unfeasible and technically unnecessary. Standard components, such as non-critical structural or mechanical elements, are governed by known historical lifetime distributions, which the authors modeled analytically using two-parameter Weibull distributions defined by specific shape and scale values. The operational reliability of these standard parts is calculated as a conditional probability based on their effective operating age accumulated prior to the break. Conversely, critical high-value subsystems, such as aircraft turbofan propulsion engines, are outfitted with continuous telemetry instrumentation that measures temperature, pressure, vibration, and mechanical wear over operating cycles, requiring data-driven analytical approaches to evaluate real-time health.

To predict the remaining useful lifetime and evaluate the reliability of sensor-monitored equipment, the investigators implemented a deep neural network utilizing a bi-directional long short-term memory architecture combined with Monte Carlo Dropout. Bi-directional recurrent neural networks capture complex temporal degradation patterns across operating cycles in both forward and backward directions, overcoming vanishing gradient issues common in standard networks. Trained on the benchmark NASA Commercial Modular Aero-Propulsion System Simulation turbofan dataset, the deep learning model maps normalized multi-sensor time-series recordings into precise component lifetime estimates. Because deterministic regression models cannot quantify residual predictive uncertainty, Monte Carlo Dropout applies stochastic dropout during the inference phase across multiple forward passes, generating a predictive distribution of remaining useful life values. This uncertainty quantification enables the direct numerical estimation of the component’s survival probability over an upcoming mission length, providing a rigorous mathematical mechanism to prevent unexpected in-flight hardware failures.

The framework also integrates an imperfect maintenance model that spans four distinct operational interventions for both component categories: do-nothing, minimal repair, imperfect maintenance, and complete renewal to an as-good-as-new condition. For standard components, maintenance effectiveness is modeled through age reduction factors that scale down the effective age of the component, thereby elevating its conditional survival probability for the subsequent operational profile. For sensor-monitored components, the researchers introduced an analogous remaining useful life extension factor, which mathematically shifts the predicted lifetime distribution based on the intensity of the repair level chosen. Minimal repairs restore failed hardware to an as-bad-as-old operating condition, whereas higher imperfect maintenance tiers restore the hardware to intermediate states between original manufacturing standards and immediate failure thresholds. Each maintenance level is tied to specific labor time requirements and associated costs, enabling the optimization routine to balance the exact degree of physical restoration against the ticking countdown of the maintenance break.

To rigorously resolve the severe risks posed by variable repair times and uncertain break durations, the researchers formulated the problem as a chance-constrained optimization model. Rather than relying on simple deterministic averages, maintenance task durations and break lengths are treated as random variables governed by known probability distributions. The chance constraint enforces that the probability of all assigned repair tasks being completed within the stochastic break window must meet or exceed a specified service level confidence threshold. Because evaluating multi-dimensional convolution integrals across multiple random variables is analytically intractable, the researchers investigated two transformation methods: Sample Average Approximation and Conditional Value-at-Risk approximation. While Sample Average Approximation models scenario realizations directly, it introduces a large number of additional binary decision variables that cause high computational times and occasional constraint violations. In contrast, the Conditional Value-at-Risk reformulation converts probabilistic chance constraints into conservative, highly tractable linear constraints utilizing auxiliary continuous variables, ensuring computational stability and strict constraint compliance.

The authors evaluated the operational performance of the mathematical framework through a numerical benchmark involving a fleet of two industrial coal transportation systems and an extensive case study of four military aircraft. In the coal transportation fleet comparison, the Conditional Value-at-Risk technique solved significantly faster than Sample Average Approximation and demonstrated consistent constraint satisfaction across varying sample sizes, never violating the prescribed confidence threshold. In the military aviation case study, each aircraft comprised four serial subsystems: propulsion engines, communication sensors, targeting equipment, and combat weaponry. Aircraft engines were designated as sensor-monitored systems trained on the NASA turbofan dataset, while all other subsystems utilized Weibull failure models and Gamma-distributed maintenance durations. Evaluating the deep learning architecture demonstrated that prediction accuracy increased markedly as components approached failure, with root mean squared error dropping below five cycles at advanced degradation stages. An inference dropout rate of 0.3 was identified as optimal, eliminating component failures during missions while preventing excessive early replacements.

Extensive simulation experiments using the aviation fleet illustrated the profound operational risks of relying on deterministic planning methods instead of chance-constrained stochastic programming. When the mathematical model was evaluated across different mean break lengths of 150, 200, and 250 hours, longer intermissions allowed for additional maintenance interventions, which lowered unassigned mission penalty costs and permitted more aircraft to deploy. In stark contrast, solving the identical maintenance challenges using only deterministic average durations produced highly misleading and dangerous operational schedules. The deterministic schedules resulted in actual task completion probabilities collapsing to fifty percent or lower, while generating substantial overtime delays. In a high-stakes military deployment or time-critical industrial environment, assuming average completion times leaves systems stranded mid-repair, directly jeopardizing fleet availability, escalating emergency operational expenditures, and failing to deliver the required operational capacity.

Further experimental analyses revealed complex behavioral shifts in system-to-mission assignments when the standard deviation of break durations widened from 10 to 70 hours, as well as when the risk preference parameter was varied. As break uncertainty expanded under an 80,000-dollar combat penalty, the model dynamically shifted assignments away from combat missions toward combined reconnaissance and logistics sorties, which carried lower configuration requirements but offered collectively superior risk-adjusted returns. When the combat penalty increased to 120,000 dollars, the algorithm prioritized the high-stakes mission despite severe duration uncertainty. Adjusting the service level parameter similarly highlighted the direct economic trade-off between risk tolerance and operational costs: requiring higher task completion confidence necessitated hiring more technicians and reducing per-worker labor allocations to protect schedules. The researchers concluded that future extensions could explore two-stage stochastic models and domain-adaptive transfer learning to apply remaining useful life models across differing operating environments where extensive historical run-to-failure telemetry is unavailable.

Subject of Research: Fleet selective maintenance and mission assignment optimization under stochastic operational uncertainty

Article Title: Optimizing predictive maintenance and mission assignment to enhance fleet readiness under uncertainty

Article References: O’Neil, R., Khatab, A., & Diallo, C. (2025). Optimizing predictive maintenance and mission assignment to enhance fleet readiness under uncertainty. Autonomous Intelligent Systems, 5(1), Article 17. https://doi.org/10.1007/s43684-025-00104-1

Image Credits: AI Generated

DOI: 10.1007/s43684-025-00104-1

Keywords: predictive maintenance, fleet management, reliability engineering, machine learning, chance constrained optimization, mission readiness, deep neural networks, uncertainty quantification, Optimizing, predictive, maintenance, mission