Critical infrastructures, such as transportation, power, water, and communication networks, are vital to a nation's economic and productive activities. Since these infrastructures are often vulnerable to failures caused by aging, natural hazards, and human-induced disturbances, it is crucial to efficiently assess their reliability over time and make necessary improvements against failures. As one of the most important measures for network reliability, all-terminal network reliability is defined as the probability that all nodes in a network are fully connected. However, as the numbers of edges and nodes increase, calculating all-terminal network reliability using an exact approach is extremely time consuming and sometimes becomes infeasible within a limited time. The technical barrier is more significant when the goal is to improve and/or maintain the reliability of an existing infrastructure network, as the reliability of the network with a time-dependent topology must be constantly evaluated and optimized sequentially. To overcome these challenges, we propose the use of Graph Neural Networks (GNNs) to efficiently estimate all-terminal network reliability and provide a sequential network optimization framework by taking advantage of Deep Reinforcement Learning (DRL). Specifically, given an existing network and available resources, the goal is to determine the best sequence of maintenance, repair, and topology changes to maximize the network's all-terminal reliability over a finite time horizon. Our numerical experiments show that the GNN model outperforms those alternatives (e.g., Deep Neural Network, Convolutional Neural Network, Monte Carlo (MC) simulation) reported in previous studies in estimating all-terminal network reliability, and the DRL framework can efficiently suggest a sequence of maintenance or improvement actions to assist decision makers in achieving their reliability goals for infrastructure systems.

A fleet of self-service systems, such as electric vehicle charging piles (EVCPs), is usually installed in a specific location. During operation, these systems are subject to random failures. However, they are usually operated without on-site staff. It is quite common that a customer may switch to other unoccupied systems for service when the initially selected system is found to have failed or fails during service. This is called failure-induced demand switching (FDS). With continuous customer arrivals and system failures, such FDS events occur repeatedly and interact dynamically, making modeling and enhancing service levels quite difficult. The challenge becomes even greater when a unique two-dimensional inspection and maintenance (IM) policy is adopted to handle the maintenance needs of self-service systems in hopes of retaining their service level with respect to long-run demand satisfaction. In this paper, we investigate the long-term service reliability of a fleet of self-service systems subject to FDS and a two-dimensional IM policy. First, we model the fleet state transition process and characterize its analytical properties. Next, we measure the fleet’s long-term service reliability and obtain the analytical expressions for crucial service level metrics, such as the expected number of failed systems, the expected length of an operation cycle, and service reliability loss due to imperfect monitoring. The managerial implications regarding the selections of EVCPs and IM policy are proposed based on a numerical study of two fleets of EVCPs in Hong Kong. These implications are expected to assist the operators in ensuring fleet service levels in the long run at a minimal operation and maintenance cost. Note to Practitioners—This paper models the service reliability of a fleet of self-service systems (e.g., EVCPs) over time. Service reliability, reflecting the fleet’s service level, is defined as the proportion of demands being fulfilled and is of the utmost concern of system operators. However, under repeated FDS due to continuous customer arrivals and system failures, it is difficult to assess the fleet’s service reliability using existing methodologies. The task becomes more challenging when failures of such systems are not perfectly detected in practice. This paper develops mathematical models and a novel two-dimensional inspection and maintenance policy to overcome the technical barriers. The models enable assessing the service reliability of various self-service systems experiencing non-constant service rates. Two case studies of fleets of AC and DC EVCPs in Hong Kong are provided to demonstrate the practical applicability of the proposed models. Indeed, the core findings of this work assist practitioners in: (i) finding the optimal maintenance policy that maximizes the fleet’s service reliability, (ii) assessing the service reliability loss due to imperfect failure detection, and (iii) evaluating the sensitivity of the optimal service reliability with respect to the customer arrival rate, system failure rate, and customer behavior in reporting system failures. We also show that the proposed models provide the exact solutions to the above-mentioned metrics when the maintenance duration is longer than the service duration.

As sensing technology advances, engineers can monitor a system's physical characteristics or performance measures for reliability assessments. The evolution of such measurements as the system deteriorates can be modeled as a collection of multivariate degradation processes. The system is considered failed when any of the degradation processes reaches its predetermined threshold. In practice, degradation data are highly variable due to unobserved environmental factors, unit-specific parameters induced by underlying frailties, and physical deterioration being a function of process covariates, such as load, ambient moisture, and temperature. The later relationships, however, are often approximated through empirical transformations such as the Arrhenius model. However, as the number of degradation processes increases, model flexibility and computational cost increases in standard stochastic process models. In this article, we propose an additive functional mixed effects and Gaussian process model that isolates all sources of uncertainty and provides flexibility to incorporate physics knowledge in the reliability modeling. A comprehensive simulation study and a case study on a tuner's accelerated degradation data are presented to illustrate the capability of the proposed model and statistical methods.

Critical systems, such as telecommunication networks, power grids, transportation networks, and supply chains, have been dramatically expanded over the past decades. To avoid significant interruptions of their services, failure-prevention technologies and strategies have been explored extensively. However, in addition to inherent faults and expected failures, such systems are subject to natural and man-made hazards. The frequent occurrences of these hazards result in an increase in the systems’ operational uncertainty as well as significant disruptions of their services. Unfortunately, the traditional reliability metrics do not adequately describe a system's performance under such hazards. There is a need for assessing the resilience of a system, which characterizes the system's performance deterioration and restoration under hazards. To date, substantial effort has been devoted to describing and quantifying system resilience from different perspectives. However, conceptual understanding and visionary transition from traditional reliability to resilience are more than just taking one step further. In this article, we briefly review approaches that qualitatively and quantitatively assess system resilience and discuss their applicable scenarios and limitations. Challenges and opportunities in system resilience modeling and enhancement, such as multihazard resilience modeling and restoration sequence optimization, are also presented so that more reliability researchers and practitioners may dive into and contribute to this important area.

Reliability testing and maintenance are essential to the reliable, economical, and safe operation of a system. So far, a variety of reliability testing and statistical methods have been used successfully in reliability analysis and improvement, and maintenance planning and scheduling using different sources of data and mathematical tools continue to improve. Over the past decades, researchers and practitioners have investigated a rich collection of reliability concepts and practiced them almost everywhere involving hardware, software, and humans. Nowadays, more effort is needed to holistically handle complex systems, effectively process big data, and ensure sustainability in product design and actual operation. In this article, we briefly review the history and developments of reliability with focuses on accelerated testing (AT) and maintenance, and discuss opportunities and ongoing efforts to meet increasing customer expectations.

Remaining useful life (RUL) prediction links prognostic and predictive maintenance (PdM) decision-making. Since the prediction result serve as the basis for subsequent decision-making, it is vital to evaluate the performance of RUL prediction result. The most popular method tends to compares the actual RUL or run-to-failure data with the prediction result. However, in many real-world applications, such ground-truth measurements are unavailable during the prediction process. To address this issue, we propose a new method for real-time credibility evaluation of RUL prediction result in the absence of ground-truth measurements. The proposed method informs decision-makers of the confidence level of RUL prediction result prior to making a PdM decision. Multiple evaluation factors, such as accuracy, consistency, and effectiveness related to credibility, are proposed to utilize the information available during the prediction process based on the underlying stochastic process. Especially, a fuzzy comprehensive evaluation method is used to determine the credibility of RUL prediction result by comprehensively considering the evaluation factors, and an entropy weight method is used to update the weight of each factor. The rationality of the proposed credibility evaluation method is demonstrated using simulation and a benchmark dataset from NASA.

To maintain a multi-component system, different dedicated service teams with different skill sets and tools are often involved. Such a relationship constitutes maintenance team coalition. In most cases, it may not be the best to plan each team's maintenance activities independently as such independent decisions may not achieve the required system-level reliability performance (RP). To balance the reliability and costs of components in achieving a high level of system RP, an efficient method is to assign a failure penalty cost to each maintenance team and then develop their optimal maintenance policy. In this article, the Shapley value is utilized for fair penalty costs allocation to avoid any interest for teams to secede the coalition, whose actual role is to evaluate the criticality level of each component in the context of coalition. Moreover, imperfect inspection and imperfect repair are quite common in practice because of limited resources, technologies and time. To address these practical concerns, a new reliability-centered hybrid preventive maintenance policy is proposed. The optimal inspection interval and age-based replacement interval are determined for each team to minimize the cost rate over an infinite time horizon. Several numerical examples illustrate that the proposed decision-making method is effective in handling such complex maintenance problems involving a coalition of dedicated maintenance teams.

Remaining useful life (RUL) prediction under time-varying operating conditions is critical to the prognostics and health management of rotating machinery. In the literature, both the degradation rate and variation of a machinery component are often assumed to be solely dependent on operating conditions. However, this strong assumption is usually violated in many industrial applications. In this article, a systematic method for RUL prediction for a rotating machinery component is developed by considering the joint dependency of degradation rate and variation on time-varying operating conditions. In particular, a system state function and an observation function are utilized to characterize the component's degradation process. A quantitative relationship between the drift and diffusion parameters is established to reflect their joint dependency on the operating conditions. A two-stage hybrid approach that jointly implements maximum likelihood estimation and least squares estimation methods is proposed to facilitate parameter estimation in model development based on offline degradation data, and a Bayesian algorithm based on online condition monitoring data is utilized for RUL prediction in online implementation. A simulation study and a real application to rolling element bearings are provided to illustrate the effectiveness of the proposed method in practice.

Research on nanowire growth with patterned arrays of catalyst has shown that wire-to-wire spacing is an important factor affecting nanowire quality. To improve the process yield and the length uniformity of fabricated nanowires, it is important to reduce the resource competition between nanowires during the growth process. In this paper, we propose a physical-statistical nanowire-interaction model considering the shadowing effect and shared substrate diffusion area to determine the optimal pitch that would ensure the minimum competition between nanowires. A sigmoid function is used in the model, and the method of least squares is used to estimate the model parameters. The estimated model is then used to determine the optimal spatial arrangement of catalyst arrays. This work is an early attempt at the physical-statistical modeling of selective nanowire growth for the improvement of process yield.

Enabling more than one function in a component provides a new cost-effective way to develop a highly reliable system. In this paper, we study the reliability of a one-shot system containing multifunctional components. Such systems have attracted increasing attention in many areas, such as ad hoc sensor networks. We derive the expressions for system reliability and reliability of each function, and formulate a redundancy allocation problem (RAP) with the objective of maximizing system reliability. Unlike constructing a system with single-functional components, the number of copies of a specific function to be included in each multifunctional component (i.e., functional redundancy) needs to be determined as part of the design. Moreover, a start-up strategy for turning on specific functions in these components must be decided prior to system operation. We develop a heuristic algorithm and include it in a two-stage genetic algorithm (GA) to solve the new RAP. We also apply a Tabu search (TS) method for solving such NP-hard problems. Our numerical studies illustrate that the two-stage GA and the TS method are quite effective in searching for high-quality solutions.

Most research on degradation models and analyses focuses on nondestructive degradation test data. In practice, destructive tests are often conducted to gain insights into the changes of the physical properties of products or materials over time. Such tests sometimes provide more reliable degradation information than nondestructive tests that may only yield indirect degradation measures, such as temperature, amount of metal particles, and vibration. However, an obvious drawback of destructive tests is that only one measurement can be obtained from each specimen. Moreover, some products start degrading only after a random degradation initiation time that is often not even observable in destructive degradation tests (DDTs). Such a degradation-free period adds another dimension of complexity in modeling DDT data. In this paper, we develop two delayed-degradation models based on DDT data to evaluate the reliability of a product with an exponentially distributed degradation initiation time. For homogeneous and heterogeneous populations, fixed-effects and random-effects Gamma processes are considered, respectively, in modeling the actual degradation of units after degradation initiation. A maximum likelihood method as well as an expectation-maximization algorithm is developed to estimate the model parameters, and bootstrap methods are used to obtain the confidence intervals of the interested reliability indices. Numerical examples demonstrate that the proposed models and estimation methods are effective in analyzing DDT involving random degradation initiation times.

Maximum releasable capacity and internal resistance are often used as the health indicators (HIs) of a lithium-ion battery for degradation modeling and estimation of remaining useful life (RUL). However, the maximum releasable capacity is usually difficult to estimate in online applications due to complex operating conditions in the field. Moreover, measuring the internal resistance is too expensive to be implemented on-line. In this paper, an HI extraction and optimization framework requiring only the operating parameters of lithium-ion batteries is proposed for battery degradation modeling and RUL estimation. The framework carries out raw HI extraction, transformation, correlation analysis, and verification and evaluation to achieve HI enhancement. In particular, the Box-Cox transformation is adopted to improve the correlation between the extracted HI and the battery's actual degradation state. To estimate the battery's RUL using the enhanced HI, an optimized relevance vector-machine algorithm is utilized, which can be performed in a flexible and agile way. Experimental studies using two different industrial testing data sets illustrate the high efficiency and adaptability of the proposed framework in lithium-ion battery degradation modeling and RUL estimation.

Multichannel sensor systems are widely used in condition monitoring for effective failure prevention of critical equipment or processes. However, loss of sensor readings due to malfunctions of sensors and/or communication has long been a hurdle to reliable operations of such integrated systems. Moreover, asynchronous data sampling and/or limited data transmission are usually seen in multiple sensor channels. To reliably perform fault diagnosis and prognosis in such operating environments, a data recovery method based on functional principal component analysis (FPCA) can be utilized. However, traditional FPCA methods are not robust to outliers and their capabilities are limited in recovering signals with strongly skewed distributions (i.e., lack of symmetry). This paper provides a robust data-recovery method based on functional data analysis to enhance the reliability of multichannel sensor systems. The method not only considers the possibly skewed distribution of each channel of signal trajectories, but is also capable of recovering missing data for both individual and correlated sensor channels with asynchronous data that may be sparse as well. In particular, grand median functions, rather than classical grand mean functions, are utilized for robust smoothing of sensor signals. Furthermore, the relationship between the functional scores of two correlated signals is modeled using multivariate functional regression to enhance the overall data-recovery capability. An experimental flow-control loop that mimics the operation of coolant-flow loop in a multimodular integral pressurized water reactor is used to demonstrate the effectiveness and adaptability of the proposed data-recovery method. The computational results illustrate that the proposed method is robust to outliers and more capable than the existing FPCA-based method in terms of the accuracy in recovering strongly skewed signals. In addition, turbofan engine data are also analyzed to verify the capability of the proposed method in recovering non-skewed signals.

The generalized renewal process (GRP) has been widely used for modeling repairable systems under general repairs. Unfortunately, most of the related work does not provide closed-form solutions for predicting the reliability metrics of such systems, such as the expected number of failures, and the expected failure intensity, at a future point in time. A technical approach reported in literature is to conduct simulations to predict the reliability metrics of interest; however, simulations can be time-consuming. To reduce computational efforts for failure prediction, we propose an analytical approach that does not rely on simulations. Our idea is to predict the system's mean residual life based on its virtual age after each repair. The predicted mean residual life is then used to determine the expected time to the next failure. To illustrate this approach, we use a log-linear failure intensity function, and provide a detailed procedure for obtaining the maximum likelihood estimates (MLE) of the model parameters. A numerical study shows that this simple yet effective approach can provide failure predictions as accurate as the simulation alternative. We then demonstrate how the proposed approach can evaluate different maintenance strategies more efficiently compared to using simulations.

Reliability Demonstration Testing (RDT) has been widely used in industry to verify whether a product has met a certain reliability requirement with a stated confidence level. To design RDTs, methods have been developed based on either the number of failures or the failure times. However, practitioners often have difficulty in determining which method to use for a specific design problem. In particular, the method based on the number of failures cannot be used when all the units are tested to failure, while the alternative based on failure times falls short in dealing with cases where no failures are expected. This paper elaborates on the two methods, and compares them from both practical and theoretical standpoints. The detailed discussions regarding the relationship between the two methods will help practitioners design RDTs, and understand when the two methods will lead to similar designs. A Weibull distribution is used in the relevant mathematical derivations, but the results can be extended to other widely used failure time distributions. Case studies are provided to demonstrate the use of the two methods in practice, and in developing equivalent RDT designs.

Condition monitoring (CM) has been recognized as a more effective failure prevention paradigm than the time-based counterpart. CM can be performed via an array of sensors providing multiple, real-time equipment degradation information with broad coverage. However, loss of sensor readings due to sensor abnormalities and/or malfunction of connectors has long been a hurdle to reliable fault diagnosis and prognosis in multichannel CM systems. The problem becomes more challenging when the sensor channels are not synchronized because of different sampling rates used and/or time-varying operational schemes. This paper provides a nonparametric sensor recovery technique and a semi-parametric alternative to enhance the robustness of multichannel CM systems. Based on historical data, models for all the sensor signals are constructed using functional principal component analysis (FPCA), and functional regression (FR) models are developed for those correlated signals. These models with parameters updated in online implementation can be used to recover the lost sensor signals. A case study of aircraft engines is used to demonstrate the capability of the proposed approaches. In addition to recovering asynchronous sensor signals, the proposed approaches are also compared with the Elman neural network as a popular alternative in recovering synchronous sensor signals.

Throughput of a manufacturing process depends on the effectiveness of equipment maintenance, and the availability of spare(service) parts. This paper addresses a joint production and spare part inventory control strategy driven by condition based maintenance(CBM) for a piece of manufacturing equipment. Specifically, a critical unit is continuously monitored for performance degradation during operation. The amount of degradation is utilized to initiate replacement actions in conjunction with spare part inventory control under both production lot size, and due date constraints. A degradation limit maintenance policy is combined with a base stock spare part inventory control policy to manage the manufacturing process. The objectives are to minimize the spare part inventory, and the expected total operating cost. Constrained least squares approximation, and simulation-based optimization are utilized, in a heuristic two-step approach, to determine the optimal base-stock level of spare parts, along with the preventive maintenance threshold. The resulting joint decision ascertains the allowed stockout probability for spare parts, while incurring the minimal operating cost for the required production within a fixed production duration. A case study of an automotive engine manufacturing process is provided to demonstrate the proposed decision-making methodology in practical use.

Numerous stochastic models for repairable systems have been developed by assuming different time trends, and repair effects. In this paper, a new general repair model based on the repair history is presented. Unlike the existing models, the closed-form solutions of the reliability metrics can be derived analytically by solving a set of differential equations. Consequently, the confidence bounds of these metrics can be easily estimated. The proposed model, as well as the estimation approach, overcomes the drawbacks of the existing models. The practical use of the proposed model is demonstrated by a much-discussed set of data. Compared to the existing models, the new model is convenient, and provides accurate estimation results