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 study focuses on predicting key quality indicators of industrial processes. In real-world applications, these indicators are crucial not only for assessing product quality but also for driving process control. Accurate and timely predictions are essential for ensuring the successful implementation of these processes. However, most current approaches rely on analytical models with simplifying assumptions, often rendering them inaccurate and rigid. These models struggle to capture and predict drifts in quality that arise from deviations from ideal conditions. This work addresses these limitations by adopting a data-driven approach that leverages the abundance of historical production data. In the context of steel manufacturing, notably the Hot Strip Mill (HSM) process, the coiling station temperature (CT) is used as an indirect gauge of material properties and, by extension, product quality. Current methods predict CT using production parameters (material composition, exit mill temperature, speed, heat of transformation and water flow distribution in the Run-Out-Table) as inputs to analytical models based on first principles, such as heat transfer and phase transformation. However, surface quality also influences CT due to its measurement via infrared pyrometers (IR). Surface defects create fluctuations in CT measurements, making it a potential indirect indicator of surface quality. Unfortunately, the simplifying assumptions of analytical models prevent them from accounting for these fluctuations, resulting in inaccurate CT predictions and missed opportunities to assess surface quality—a critical factor for steel users. This study overcomes these challenges by adopting a data-driven approach that relaxes the assumptions of traditional analytical models. Historical production data inherently capture the relationships between process parameters and quality indicators. Data-driven models, particularly neural network regressors, are flexible enough to uncover these connections without predefined assumptions, enabling them to account for most quality deviations and provide more accurate, comprehensive predictions. To achieve this, production data for a selected steel grade that presents CT fluctuations were collected and curated. Neural network regressors were trained using the curated production data, with custom loss functions and performance metrics designed to improve prediction accuracy. These tailored tools address the challenge posed by data distributions that are centered on normal values, where deviations rarely occur. The custom functions and metrics ensure precise capturing and identification by targeting these rare but critical deviations. They help minimize the risk of misidentifying significant temperature anomalies, further enhancing the accuracy of the predictions. Physics and domain knowledge were also integrated into the data-driven models to further improve performance and reliability. The resulting CT predictions can enable high-performing proactive control and pave the way for improved process efficiency and product quality.

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. Production system operation is often affected by dynamic conditions and maintenance limitations. While most research focuses on preventive replacement maintenance, this paper introduces an imperfect condition-based maintenance policy tailored for systems subject to dynamic environmental conditions. The degradation of the system due to environmental changes is modeled using a L\'evy process derived from a gamma process, compound Poisson process, and embedded Markov chain. Periodic inspections allow maintenance actions to be triggered based on the observed degradation level. When degradation exceeds a predefined threshold, imperfect preventive maintenance is performed, partially restoring the system's degradation. To minimize the long-term average maintenance cost, we optimize the combination of inspection interval and preventive maintenance threshold using an enhanced Cyclic Coordinate Search algorithm. A case study on wind turbine bearings and sensitivity analysis demonstrate the proposed maintenance policy and underscore the value of proactive maintenance under harsh environmental conditions and increased maintenance effectiveness.

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. 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. 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. 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. 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. 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. 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.