ABSTRACT. Optimizing maintenance strategies is critical for ensuring the safety, reliability, and cost-effectiveness of aircraft operations. A fundamental challenge in predictive maintenance lies in quantifying the impact of maintenance interventions. Existing approaches for evaluating this impact generally fall into two categories: model-based methods, which rely on predefined mathematical formulations but often fail to capture real-world complexities, and data-driven methods, which leverage real-time monitoring data but function as black-box models without explicitly characterizing maintenance effects. This lack of interpretability and generalizability limits their practical application. To address these challenges, this paper introduces a novel self-supervised learning approach for interpretable maintenance impact quantification. Particulerly, by employing a Siamese architecture with interpretable Boltzmann Knowledge-Action Networks (KANs), the proposed framework derives an analytical expression that quantitatively describes maintenance effects. This allows for a transparent and physically meaningful assessment of maintenance efficiency, bridging the gap between data-driven adaptability and model-based interpretability. Experimental evaluations on real-world aircraft maintenance datasets demonstrate that the proposed approach outperforms traditional methods in predicting post-maintenance system health while offering a clear, explainable rationale for its predictions. These findings highlight the potential of interpretable deep learning models to enhance predictive maintenance, ultimately supporting more informed decision-making and improving aviation safety and efficiency.

ABSTRACT. The desalination industry is multi-million dollar, and its benefits are crucial for daily life and industrial applications. However, the complex problem that desalination systems face is that the system encounters issues related to biofouling, which reduces desalination efficiency and causes too high maintenance costs. Accurately predicting the condition of the membrane and its changes after applying cleaning methods will help manufacturers find practical and cost-effective solutions. Thus, this paper researches and then develops a physic-informed deep learning model that incorporates information about physical law in constructing the loss function to increase the prediction performance in the desalination system. In addition, incorporating physical information helps improve the certainty of the prediction and reduces the requirement for the amount of data collected. The experiments were done to evaluate the promise of the proposed model.

ABSTRACT. High-tech machines are highly complicated machines containing many interacting parts and exhibiting few (rare) failures, with high heterogeneity (partly due to the plethora of underlying failure causes). This makes predicting the expected number of future failures per time unit in an operational fleet of machines challenging, and thus hinders a cost-effective stocking and maintenance strategy. This article explores the benefits and drawbacks of popular statistical models within the high-tech industry for modeling rare failures. In this effort, the article should be viewed as a point of practical inspiration and not as a complete literature overview of the status-quo.

ABSTRACT. This paper addresses the practical problem of unscheduled maintenance. Unscheduled maintenance needs may arise either due to natural reasons, inadequate/improper maintenance, or a lack of support resources needed to turn around an asset. One of the possible solutions to this problem is to adopt or improve preventive maintenance strategies. This paper uses the concept of delay time modeling (DTM) to address the practical problem mentioned earlier. An extension of the basic DTM has been used, and downtime and cost models have been developed to factor in supportability requirements. The TOPSIS multi-criteria decision model has been used to refine the inspection interval results of the cost and downtime models to obtain the ideal inspection interval in line with an organization’s preference. Finally, the ‘risk’ element has been factored in to validate the computed ideal inspection interval and make the model acceptable to other industries.

ABSTRACT. Predicting the degradation and ageing of materials in a system is important as it will allow us to establish the lifetimes and the material options for replacement / extension programmes. The calculation of long-term ageing is challenging due to numerous issues with material and species interactions. Experiments finding properties such as diffusivity and solubility of materials are relevant in advancing understanding of the mechanisms. Water vapour is a key species of interest as it may degrade components as it is absorbed and may cause physical and chemical property changes, thus limiting their useful lifecycle. Dynamic Vapour Sorption experiments are conducted to understand material characteristics of small samples, normally considered to exhibit 1D diffusion. This then allows the model parameters obtained from these experiments to be applied to 3D samples, removing the need to test unfeasibly large and expensive components. Here we consider the best way to analyse raw experimental results by fitting to three different models, (1) an analytic model with constant boundary conditions (2) a single mode model based on Fick’s equation and (3) a dual mode model extending (2) by consideration of Langmuir adsorption. Each of these has a different level of complexity and insight.

ABSTRACT. In the hydropower industry, traditional reliability models are limited by failure data availability and quality. This research prepares for a Bayesian Stochastic Petri Net (BSPN) model for two assets: a spillway gate and an alternator. Maintenance records, inspection results, and operational data were compiled and analysed to assess the possibility of determining the parameters necessary for the BSPN development, such as the state transition probabilities and the relevant input variables for Bayesian updates. It was determined that the data was insufficient to make strong statistical inferences from. An alternative approach is proposed using simulated data to create the model.

ABSTRACT. For the energy pipeline industry in particular, pipeline wall condition assessment is crucial to what they term integrity management. Failure to detect a defect (localised reduction in wall thickness) or to accurately predict defect growth can lead to catastrophic failure. Industry seeks practical modelling techniques compatible with available data. Relevant types of data informing defect prediction that is normally available includes environmental, operational, construction parameter, and various types of condition data. Increasingly, reliable condition data generated by ‘in-line-inspection’ (ILI) is available. The cost of ILI precludes frequent use resulting in scare data: perhaps 2 to 5 data points per site. This prevents the practical application of complex modelling techniques for the prediction of specific defect growth. We report a study exploring on the use of simple models of each with two or three parameters. Five simple models were tested using the ILI datasets collected from three energy pipelines. It was found that these models can present reasonable prediction accuracy, with the logarithmic model returning the best prediction accuracy of approximately 80%. Based on the test outcome, a framework is proposed that guides individual defect growth prediction in industrial practice. The framework can be integrated into existing industry-workflows, enabling practical implementation to enhance operational safety and decision-making in pipeline operation.

ABSTRACT. Power transformers are crucial for modern electrical grids, and their reliable operation is vital for ensuring uninterrupted power supply and preventing costly failures. Transformer faults, if undetected, can lead to catastrophic failures and expensive repair costs. Dissolved Gas Analysis (DGA) is an effective diagnostic technique that monitors key gases produced during insulation degradation and fault conditions. Traditional DGA methods, such as the Rogers Ratio, Doernenburg Ratios, Key Gas Method, and Duval Triangle, provide insights but lack a unified index for overall transformer health assessment. This study evaluates the health of oil-immersed transformers through empirical DGA data analysis and introduces the Dissolved Gas Analysis Factor (DGAF) as a consolidated health metric.

A dataset of 871 DGA samples from 240 oil-immersed power transformers was analyzed, categorizing fault conditions into Partial Discharge (PD), Low-Energy Discharge (D1), High-Energy Discharge (D2), Medium-Temperature Overheating (T2), High-Temperature Overheating (T3), Discharge-Thermal (DT), and Normal Condition (N). Correlation analysis was conducted to explore relationships between individual gas concentrations, and a novel DGAF was developed for comprehensive health assessment. Statistical analysis examined the trends of seven key gases (H₂, CH₄, C₂H₆, C₂H₄, C₂H₂, CO, CO₂) under various fault conditions. The results indicated that hydrogen (H₂) exhibited a significant increase in Partial Discharge (PD) cases, while high-energy discharge (D2) and overheating faults (T2, T3) showed substantial increases in H₂, CH₄, C₂H₆, and C₂H₄ levels.

To enhance the accuracy of transformer condition assessment, the DGAF model was developed using weighted scoring system, assigning scoring factor (S) and weighting coefficients (W) to individual gases. The condition score for each gas, is determined by the IEC/IEEE standards (IEC Standard 60599-2007, IEEE C57.104-2019, Prasojo et al. 2020; Tamma et al. 2021; Li et al. 2023). These parameters were optimized to improve DGAF's sensitivity in distinguishing between minor and severe faults (Ashkezari et al. 2012; Haema et al. 2013; Murugan et al. 2019).

The study also introduced a refined classification system for transformer health assessment based on DGAF, categorizing conditions into Good (DGAF < 1.2), Acceptable (1.2 ≤ DGAF < 1.5), Need Attention (1.5 ≤ DGAF < 2), Poor (2 ≤ DGAF < 3), and Very Poor (DGAF ≥ 3) (Jahromi et al. 2009; Haema et al. 2012, Brandtzæg 2015, Wattakapaiboon et al. 2016; Prasojo et al. 2020).

A probabilistic fault assessment model, P(Fail), was also formulated based on DGAF distributions, enabling a quantitative prediction of transformer failure risks.

Validation on an extended dataset showed that DGAF-based classification achieved high accuracy in fault detection and health assessment. The results confirmed that DGAF offers a more comprehensive measure of transformer condition than conventional DGA methods. The refined DGAF scoring system supports more precise predictive maintenance strategies, allowing utilities to take proactive measures before critical faults occur.

These findings highlight DGAF's potential as an advanced health index for power transformers, facilitating early fault detection and improving predictive maintenance decision-making. Future research will focus on integrating DGAF with artificial intelligence (AI) and machine learning algorithms to enhance real-time fault prediction and optimize transformer monitoring systems. By leveraging data-driven health assessment models, power utilities can significantly improve transformer reliability, reduce downtime, and enhance grid stability.

ABSTRACT. We study a maintenance policy oriented to technical systems with multiple components arranged in complex configurations. Such configurations often present a challenge for maintenance management, as different components may have a different level of importance for the functioning of the system as a whole. The proposed policy incorporates block replacement and opportunistic maintenance approaches within an adaptive framework. A mathematical model was developed to evaluate the maintenance policy performance, considering the balance between execution costs and operational risk management. This work was motivated by a case study on the maintenance of a manifold valve used in a production line of a food industry. A numerical application is presented, showing the advantages of the proposed model for structuring a maintenance policy.

ABSTRACT. Protection systems are critical for preventing catastrophic failures, often acting as the last line of defense in extreme conditions. Their reliability is essential to avoid severe safety, environmental, or economic consequences. This study proposes a model for a non-repairable protection system, where inspections are performed at fixed intervals. The model integrates two key features: (i) the delay-time inspection concept to address internal deterioration, and (ii) shock effects to account for external factors, such as mechanical vibrations, that impact reliability. By evaluating inspection policies, the model balances system reliability and maintenance costs, highlighting the importance of proactive strategies to ensure these systems function effectively when demanded during critical events.

ABSTRACT. In the food industry, maintenance policies play a pivotal role not only in ensuring cost-efficiency but also in safeguarding product safety and quality. This study proposes a delay-time-based hybrid inspection maintenance policy specifically adapted to the unique demands of the food industry. The case study focuses on a critical component of a vacuum packing machine in meat production. This component, when in a failed state, prevents proper sealing of vacuumed meat packages, and in a defective state, produces weak seals that can compromise food safety. The proposed policy integrates quality and maintenance inspections to proactively address these issues, reducing the reprocessing of meat cuts and preventing defective products from reaching supermarket shelves. At the same time, it aims to minimize maintenance costs and operational downtime. Furthermore, the model leverages replacement opportunities arising from internal and external sanitation audits, enhancing the flexibility and responsiveness of the maintenance strategy. This tailored approach ensures the system remains under control, ultimately supporting both economic performance and food safety compliance in the meat processing industry.

ABSTRACT. This paper proposes a preventive inspection and replacement policy for a protection system composed of two interdependent components. One component is responsible for detecting anomalies in the system and sending a signal to the second component, which automatically intervenes to interrupt the flow and protect the main system. While the first component acts as a sensor and controller, the second component performs the interruption of the flow in the event of a fault. However, if the first component fails, it will compromise the operation of the second component, as it will no longer provide the necessary signals, resulting in a "defect" in the second component. The dynamic system environment is modelled considering that the first component is subject to both internal degradation and external shocks, while the second component is affected only by internal degradation. It is assumed that, under demand, a fully functional second component meets 100% of the demand, while a defective second component, with reduced capacity, only meets the demand partially. The proposed maintenance policy aims to ensure the continuous readiness of the components. The performance of the proposed policy is studied under different parameter settings to assess its effectiveness.

ABSTRACT. In many industrial applications, continuous condition monitoring and periodic inspections are impractical due to harsh environments, inaccessibility, or excessive costs. Other traditional maintenance strategies such as time-based preventive maintenance (PM) and run-to-failure corrective maintenance (CM) can be used, but they often fail to balance cost efficiency and reliability when failure is unpredictable. This paper proposes a threshold-based hybrid maintenance strategy, where imperfect corrective actions are performed up to a predefined number of consecutive failures, after which a full preventive replacement is triggered. This approach leverages the history of degradation events to inform maintenance decisions without requiring real-time monitoring. The proposed method is particularly relevant for systems such as sealed industrial bearings, offshore oil & gas components, hydraulic actuators in mining equipment, and aerospace cabin safety systems, where degradation is stochastic and difficult to track. Unlike fixed-interval PM, which can lead to premature replacements, or pure CM, which results in excessive downtime, our strategy dynamically integrates both methods by adapting maintenance actions to observed failure frequencies. Through numerical simulations based on gamma-process degradation modeling, we aim to demonstrate that a failure-threshold-based policy significantly outperforms fixed-time replacements under high degradation variability. The results could highlight a critical gap in maintenance optimization research, where the combination of preventive and corrective actions in systems lacking direct condition monitoring remains underexplored. The findings could offer valuable insights for decision-makers seeking cost-effective maintenance strategies in unpredictable operational environments.

ABSTRACT. Boiler Force Draft Fan Gearbox tripped due to excessive temperature at the pinion gear outboard bearing. Upon investigation, water contamination was found in both the bearing housing and the lubrication system, traced back to a GTS leak from the associated steam turbine utilizing the FRACAS fault tree analysis and the 5-whys Root Cause Analysis methodology. While most leaking steam escaped into the atmosphere, a portion entered the bearing housing where it condensed into water and spread through the lubrication system via the steam turbine bearing housing drain. This contamination compromised the lubricants ability to maintain proper oil film lift and thermal dissipation, leading to excessive temperatures and accelerated deterioration of the bearing babbitts. As a result, the machine’s bearings suffered from a 6-month Mean Time Between Failure (MTBF) index, generating a high maintenance cost.

To address this issue and enhance equipment reliability, a pressurized air system was introduced into the bearing housing, acting as a barrier medium to prevent steam ingress. This simple yet effective solution has eliminated water contamination while preserving lubricant quality and ensuring optimal bearing performance. Since implementation, the lubrication system has remained moisture-free leading to improved reliability and extended operational availability of the machine. This entirely-in-house-developed modification does not only prevent premature bearing failures but also ensures the continuous operation of the critical plant equipment, supporting uninterrupted steam production. The implementation of this idea has resulted in a notable cost-avoidance of more than 30,000$ per bearing per equipment. This case highlights the impact of innovative reliability improvements and demonstrates the effectiveness of air barriers in protecting lubrication systems from contaminants.

ABSTRACT. Abstract Enhancing the reliability of rotating equipment is crucial for minimizing downtime and maximizing operational efficiency in industrial settings. This study presents advanced methodologies aimed at improving the reliability and longevity of rotating equipment at Saudi Aramco, focusing on repair techniques for shafts and critical components. The discussion includes various methods such as welding build-up techniques, sleeve installations, High-Velocity Oxygen Fuel (HVOF) coating, and laser cladding. These techniques restore original geometry, improve wear resistance, and extend service life. A case study showcasing the application of these methods on damaged rotating shafts highlights their practical benefits in enhancing equipment performance. Keywords: Rotating Equipment, Shaft Repair, HVOF Coating, Laser Cladding, Reliability Enhancement. 1. Introduction The performance of rotating equipment such as pumps, compressors, turbines, and motors is essential to industrial operations. Failures in shafts and other critical components can lead to costly downtime and maintenance. This paper explores repair methodologies that extend the service life of rotating equipment while maintaining performance and reliability. Salvaging rotating equipment shafts is a cost-effective and sustainable approach that helps industries reduce maintenance costs, minimize equipment downtime, and optimize resource utilization. Manufacturing new shafts from raw materials is expensive and time-consuming, often requiring long lead times for procurement and fabrication. By implementing advanced repair methods such as HVOF coating, laser cladding, and weld build-up, industries can restore worn or damaged shafts to their original specifications while enhancing their durability and performance. 2. Shaft Repair Methods Various techniques are available for repairing damaged rotating shafts, each offering unique advantages depending on the extent of wear and operating conditions. 2.1 Welding Build-Up This method involves applying additional material via arc welding (TIG, MIG, stick) to restore shaft dimensions. It provides a strong metallurgical bond but may introduce heat-affected zones (HAZ) that require post-weld heat treatment. 2.2 Sleeving Installation A worn shaft section can be repaired by installing a precision-fit sleeve, either by press-fitting or using adhesive bonding. This method is quick and effective for moderate wear but may reduce overall shaft strength. 2.3 High-Velocity Oxygen Fuel (HVOF) Coating HVOF spraying is a high-energy process that produces dense, wear-resistant coatings. It offers minimal heat input and high bond strength, making it ideal for high-speed rotating equipment like pump shafts and compressor rods. 2.4 Laser Cladding This advanced method uses a laser to fuse powdered or wire-based coatings onto the shaft, achieving excellent adhesion and minimal distortion. Although it is costly, it is highly effective for precision applications in aerospace and nuclear industries. 3. Case Study: Shaft Repair in Rotating Equipment A case study at Saudi Aramco involved the repair of a severely worn compressor shaft. The original shaft had deep wear marks and corrosion damage due to prolonged exposure to high-temperature and acidic environments. 3.1 Repair Methodology •Inspection & Damage Assessment: Identified wear depth and material composition. •Coating Selection: HVOF with Diamalloy 5803 was chosen for superior corrosion resistance. • Application Process: The shaft was grit blasted, HVOF-coated, and post-machined to precise dimensions. •Performance Evaluation: After installation, vibration analysis confirmed improved reliability. 3.2 Results •Increased service life by 3× compared to uncoated shafts. •Reduced maintenance frequency, leading to lower operational costs. •Improved resistance to corrosion and abrasive wear. 4. Conclusion Advanced repair techniques such as HVOF, laser cladding, and plasma spray significantly enhance the reliability and longevity of rotating equipment. Selecting the right repair method based on damage severity and operating conditions ensures cost-effective maintenance while minimizing downtime. Industries such as oil and gas, aerospace, and power generation can greatly benefit from these cutting-edge technologies, improving equipment performance and reducing total lifecycle costs. References [1] W-18 Saudi Aramco welding & Coatings; High Velocity Oxygen Fuel of Thermal Spray Coating [2] W-19 Saudi Aramco Welding Procedure Specification Guidelines [3] S-04 Shafts; Shafts Repair Method Selection Procedure: Surface Damage [4] S-09 Shafts; Salvage of Used Shaft Material

ABSTRACT. Highly complicated machines contain many parts with few failures (up to 5 in the whole history). This makes predicting future failures challenging, hindering a cost-effective stocking and maintenance strategy. This article explores the benefits of switching from the traditional Poisson to the Zero Inflated Poisson (ZIP) distribution for the modeling of the occurrence of rare failures. Using real data, we compare the performance of the two modeling approaches and show that the proposed model significantly improves the forecasting accuracy of spare part storage management. ZIP also provides an improved prediction range that more accurately describes the magnitude of predicted failures.

ABSTRACT. Transmission system operators (TSOs) must balance the renewal of aging infrastructure with integrating renewable energy sources. Traditional age replacement models assume identical replacements and often overlook financial factors like discounting. This work introduces a model based on the delayed renewal reward process, showing that the optimal replacement age of the first asset depends on both existing and replacement asset characteristics. It also highlights that such an optimal age exists only if discounting is considered. Moving beyond traditional assumptions provides TSOs with more realistic, cost-effective asset management strategies in a changing energy landscape.

ABSTRACT. Hidden Markov Models appear in many real-world estimation problems where a process with unobservable states produces observable outputs (indicators or signals) that are related to the process hidden state. In this work we consider a Continuous Time Hidden Markov Model to model the degradation process of a system of interest. The current state of the system is not directly observable, but it is estimated based on the available signals, for example indicators of temperature or pressure provided by a sensor.

The system considered is maintained throughout its life. We are interested in knowing how well the maintenance action performed recovers the system. We proposed some measures to estimate the effectiveness of the maintenance as well as reliability measures. The proposed measures are based on estimators of the model parameters obtained via a discretization strategy, that is, we consider that the signals are produced continuously but only observed at regular intervals of time.

ABSTRACT. Cities rely on sewer pipe infrastructure to dispose of water and waste. To avoid failures, inspections, maintenance, and replacements need to be planned. Inspections assess the sewer pipe’s condition on various failure modes. Maintenance can improve the condition on some failure modes, but at some point replacements must be planned to avoid failure. We formulate the inspection, maintenance, and replacement problem as a partially observable Markov decision process. We use a PO-MDP instead of an MDP because inspections are not done in each period and hence we have no full information in each period on the state of the system.

We perform a case study based on real-world data and parameters established together with an expert. Using an open-source solver, we obtain near-optimal policies. For a sewer pipe at a location with a low failure cost, the policies inspired by practice perform at least 34% worse than the near-optimal policy. For a sewer pipe at a location with a high failure cost (e.g. at an important traffic junction), the policies inspired by practice perform at least 2.5 times worse than the near-optimal policy. Our results imply that large cost savings can be realized by making the planning dependent on the failure cost of the sewer pipe and on its (partially observed) condition.

ABSTRACT. Degrading systems typically consist of interconnected components that significantly affect their overall performance. An example of this is lighting systems made up of numerous LED lamps, which exhibit a dependence due to their common usage. To address degradation and extend the lifespan of these systems, maintenance actions are implemented. This work explores the concept of imperfect maintenance actions through the Arithmetic Reduction of Degradation (ARD) model, which means the reduction of the total accumulated degradation in the system from its installation. In this context, we analyze the inference problem in a two-component degrading system, where degradation follows a bivariate Wiener process. The dependence between components is modelled using the trivariate reduction method, and parameters are estimated using the maximum likelihood approach. Traditionally, parameter estimation in degradation models relies on degradation or failure observations. However, this work introduces a novel approach by estimating model parameters based on maintenance data. We assume that maintenance information is collected in an unbalanced design, indicating that data from the two degradation processes may not be measured simultaneously. Different observation strategies are examined, allowing for the assessment of degradation levels both between maintenance actions and immediately before or after these interventions.

ABSTRACT. The optimization of predictive maintenance models is a crucial issue for the industrial vehicle sector, in particular when taking into account operational constraints such as resource management, circularity and customer expectations. This research focuses on the modeling and optimization of maintenance policies, an area that has become essential for automakers, who have become aware of the importance of after-sales services in their revenues. Customers' expectations have also evolved: they are no longer content with simple breakdown alerts; they are now looking for comprehensive, optimized maintenance solutions, aimed at limiting workshop visits, avoiding breakdowns and unscheduled downtime, while ensuring that their missions are fulfilled. The aim of this research work is to develop an optimized predictive maintenance model that explicitly integrates operational constraints. These constraints include circularity, which allows for the replacement of parts with remanufactured or reconditioned parts in addition to new parts. Furthermore, availability constraints are also considered, referring to the stock availability of parts, whether they are new or remanufactured. This model aims to optimize maintenance decisions while maximizing operational efficiency and minimizing associated costs, all while meeting customer expectations regarding reliability. Maintenance modeling will be carried out over a finite horizon, corresponding to the duration of the maintenance contract with the customer. First, we will define what is a remanufactured component and analyze its impact on the level of system degradation. We will then integrate into the same maintenance model the consideration of parts availability in the replacement decision-making process. The proposed maintenance policy will take account of available stocks and provide a maintenance schedule based on this availability. In addition, we propose to consider the recovery of the vehicle after the term of the contract. Optimization will therefore be carried out on the total cost of maintenance throughout the life of the contract, taking into account whether the vehicle will be recovered after the end of the contract. These optimizations and modeling will be carried out using simulations, and the results obtained will be used to assess the effectiveness of circularity in a maintenance model. We will also examine how the addition of the availability constraint allows us to opt for a more complete model, offering additional gains and better-planned workshop interventions. In conclusion, this study shows how predictive maintenance can be optimized by considering both circularity and spare parts availability within a finite maintenance horizon. Using dynamic programming, we will simulate different scenarios to evaluate the performance of the system over time and optimize the maintenance policy. This approach ensures that maintenance decisions are not only cost-effective, but also environmentally sustainable by balancing the compromise between operational efficiency and resource availability. Ultimately, this method provides a robust framework for sustainable predictive maintenance that meets both operational needs and sustainability goals.

ABSTRACT. The operational performance of naval ships relies on their deployment and maintenance. The deployment is the assignment of specific missions to a specific ship. The missions indicate the type of use and the type of (weather) conditions in which the naval ship is deployed. The type of use and conditions influence the system degradation and in turn this has an influence on the maintenance needed. Maintenance needs are also affected by prescribed protocols and the present condition of the ship.

Planning the deployment in accordance with maintenance, therefore, is an intricate challenge. Determining the best moment for maintenance is difficult when one does not want to interfere with the ship deployment. But it is also difficult to plan the deployment while knowing that without performing interim maintenance future missions might not be feasible. Both deployment and maintenance need to be scheduled simultaneously in order to achieve optimal availability of naval ships. They are also both needed to maximize the percentage of successful missions.

This research focuses on ways to jointly plan maintenance and deployment, with the objective to optimize the availability of navy ships and maximize the percentage of successful missions. A mathematical optimization model has been created that allows the joint optimization of both deployment & maintenance. Based on preliminary research a Markov Decision Process (MDP) has been selected as the most suitable approach. This powerful mathematical framework can be used to model (sequential) decision-making when outcomes are partly random and partly under control of a decision-maker.

The created mathematical model will be demonstrated on a case study for the Royal Netherlands Navy. Results are used to advise on planning of maintenance and deployment.

ABSTRACT. We proposed a hybrid inspection and preventive replacement policy for technical systems subject to two types of opportunities: (1) opportunities to advance inspections at a lower cost, which occur more frequently since inspections demand less effort and time; and (2) opportunities to advance preventive replacements. The policy also allows for postponing planned preventive replacements in the case of operational constraints. To evaluate the proposed policy, we developed a mathematical model based on the delay-time concept, assuming perfect inspections. The expected cost-rate, availability, and mean time between failure events are evaluated, and the impact of uncertainties in parameter estimation is assessed through global sensitivity analysis. A numerical study is presented to demonstrate the policy's performance. Additionally, a web application is provided, allowing users to perform analyses. The policy was designed to integrate well with the working conditions of the system’s operational environment and proved to be a competitive alternative, especially in the context of manufacturing plants, where it enables better coordination between maintenance and production management.

ABSTRACT. Training large language models (LLMs) on GPU clusters demands high reliability to minimize costly downtime. While Direct- to-Chip Liquid Cooling (D2C-LC) improves energy efficiency, failures in cooling components gradually degrade performance of GPUs. This paper addresses this challenge by proposing a novel Piecewise Deterministic Markov Decision Process (PDMDP) for opportunistic maintenance optimization in D2C-LC-equipped GPU clusters. Our approach models system deterioration using a Piecewise Deterministic Markov Process (PDMP), considering load-sharing effects and random shocks from cooling component failures. We formulate an optimization problem to minimize maintenance costs and develop a simulation-integrated policy iteration algorithm for its solution. A comprehensive case study demonstrates the effectiveness of our framework in achieving optimal maintenance strategies and reducing downtime.

ABSTRACT. This paper presents a comprehensive framework for prognostics and maintenance optimization of load-sharing k-out-of-n:G systems. First, we propose a model-based prognostic approach to directly evaluate the reliability of a load-sharing system with identical components, where the remaining components equally share the load upon failures. The method leverages the step-stress accelerated lifetime model, treating component failures as "stress" events that impact system reliability. By assuming the component lifetime distribution belongs to the Gurvich family, encompassing a broad range of distributions such as Weibull, Lomax, and Burr XII, the proposed approach is applicable to a wide variety of reliability scenarios without being constrained to a specific distribution. Based on this framework, we derive the remaining useful life (RUL) of the system, a critical metric in prognostic and health management, and estimate its parameters using the maximum likelihood method.

To further enhance maintenance decision-making, we introduce a model-free reinforcement learning (RL) strategy to identify optimal maintenance policies. This data-driven approach adapts to system dynamics without relying on explicit reliability models, offering flexibility in complex or uncertain environments. The performance of the model-free RL strategy is compared with the model-based prognostic approach, highlighting their respective strengths and limitations. An illustrative example demonstrates the effectiveness of both methods, showcasing their applicability in real-world scenarios.