Integrated circuit (IC) marking detection faces critical “Triple C” challenges: compact marking scales, complex multidirectional layouts, and costly annotation requirements. Traditional models struggle with data scarcity in dynamic manufacturing environments where fine-grained labeled data are expensive and time-consuming to obtain. This work presents MarkingVLM, a specialized vision-language model designed for IC marking detection with exceptional few-shot learning capabilities. MarkingVLM adapts cross-modal understanding from Contrastive Language-Image Pre-training (CLIP) through unique innovations: 1) dual-granularity detection combining patch-level semantic alignment with pixel-level visual decoding; 2) layout mirror module enabling efficient multidirectional text flow recognition through feature-level augmentation; and 3) enhanced prompt engineering with learnable contexts for effective domain adaptation. Extensive experiments across two IC marking datasets with distinct characteristics substantiate superior performance: 94.2% precision and 96.5% recall on Dataset-1, and 89.6% precision with 92.6% recall on the more challenging Dataset-2. Most significantly, MarkingVLM achieves 92.7% precision with 32 training samples and maintains over 80% recall with merely 8 samples, demonstrating notable data efficiency improvement over conventional methods. Results establish a new paradigm for industrial text detection by bridging open-domain vision-language knowledge with specialized manufacturing requirements.

Islanded microgrid formation (IMF) enhances active distribution network resilience but is challenging for current mathematical optimization methods due to its mixed-integer nonlinear nature. Deep reinforcement learning (DRL) also struggles with complex IMF problems due to action space explosion and environmental nonstationarity. This article proposes a multiagent DRL (MADRL) method for IMF, incorporating probability space optimization and random sequential updating to address IMF problems with numerous switches. Specifically, a multiagent framework models each controllable switch as an independent agent, and a specific actor-critic network architecture is designed for discrete control problems. To achieve unbiased policy gradient estimation, a probability space optimization loss function is devised to replace the Gumbel-Softmax-based gradient estimation in existing action-aware discrete DRL algorithms. Combined with the random sequential updating mechanism, the environmental nonstationarity issue faced by each agent is effectively mitigated. This results in a discrete MADRL-based IMF strategy with high computational efficiency and stable convergence, even when numerous switches are involved. Case studies on a modified IEEE 123-node system demonstrate that this method achieves optimality ratios of 96.85% and 97.41% in 16-switch and 23-switch scenarios, respectively.

The increasing complexity and interconnectivity of modern industrial machinery, together with persistent demands for operational efficiency, have elevated reliable remaining useful life (RUL) prediction to a cornerstone of industrial intelligence. To this end, multimodal monitoring has been widely adopted, as it provides complementary perspectives on system health. Although numerous studies have exploited multimodal data to enable holistic condition assessment, most existing approaches remain fundamentally deterministic, yielding single-point estimates that are often overconfident and potentially misleading-particularly in safety-critical or cost-sensitive scenarios. To fill this trustworthy gap, a multimodal evidential learning framework is proposed with uncertainty-calibrated fusion. It integrates heterogeneous monitoring modalities by jointly exploiting scarce labeled run-to-failure trajectories and abundant unlabeled operational data. Each modality is modeled using a high-order evidential distribution, which enables an explicit analytical decomposition of predictive uncertainty into aleatory (data-driven) and epistemic (model-driven) components. These modality-specific evidential representations are subsequently fused through an uncertainty-aware mechanism. Experiments on multimodal run-to-failures of robotic harmonic drives validate the proposed framework's performance in both predictive accuracy and uncertainty quantification. Furthermore, ablation studies and comprehensive comparisons with state-of-the-art methods substantiate the contributions of individual modules and confirm the overall framework's suitability as a trustworthy decision-support tool for industrial applications.

Condition-based maintenance (CBM) has attracted significant attention in advanced manufacturing systems. In practice, degradation of production units is often influenced by their production rates. Unlike traditional CBM models that treat maintenance optimization as a stand-alone problem, we develop a joint optimization model of condition-based maintenance and production for multi-stage manufacturing systems. The resulting joint dynamic optimization problem is formulated as a Markov decision process (MDP) with the aim at maximizing the expected total production benefit. To address the curse of dimensionality and improve scalability in decision-making, a hierarchical multi-agent reinforcement learning framework is put forth to solve the MDP, leveraging a two-level architecture that decomposes the problem into manageable subtasks for maintenance and production. A distributed training strategy is introduced to independently train stage-level agents, significantly improving scalability. Experimental results from a semiconductor manufacturing facility demonstrate that the proposed joint dynamic optimization method significantly improves production benefit by maintaining a balance between production efficiency and system reliability.

This study presents ICMarkingNet, an end-to-end model for integrated circuit (IC) the marking inspection task. The model pinpoints markings against an IC image utilizing a saliency-guided regime under weakly supervised learning. Through the introduction of a novel direction representation alongside a transform-based rotation method, the model achieves improved accuracy in recognizing marking directions. Furthermore, the incorporation of a newly introduced sampling method, namely LinkSampling, enables the model to extract character features with high consistency, and empowers the model to excel in word-level marking recognition tasks. Notably, ICMarkingNet is uniquely engineered to function within a compact and streamlined pipeline, facilitating execution entirely on graphics process units. Experiments on a real-line IC marking dataset exhibit an f1-score of 96.88% and the inspection speed surpassing 100 samples per second, validating the superior performance and efficiency of the proposed model over both general end-to-end text recognition models and existing IC marking inspection frameworks.

Power systems are well-engineered systems designed to supply power generation and services to end users. They are considered as the most crucial infrastructures in modern societies as numerous facilities such as telecommunication, transportation, public health, and emergency services heavily rely on a continuous power supply for their normal operation. The complex structure and interconnection with other facilities make power systems vulnerable to external threats such as natural disasters, extreme weather, and vandalism. On the other hand, with the advancements of artificial intelligence in the recent years, various cutting-edge control and optimization methods are emerged. Among them, deep reinforcement learning (DRL) is the most promoted for enhancing power system resilience. In this context, this article performs an in-depth review of various DRL methods and their applications in resilience optimization and enhancement of power systems. The review offers a structured examination of DRL methodology, along with a systematic categorization of existing literature into three themes (proactive actions, emergency response, and restoration and recovery) according to their contingency stages. The strengths and limitations of DRL-based resilience enhancement strategies are discussed across robustness, scalability, interpretability, and safety. A research roadmap is provided to highlight possible avenues for further exploration.

In system reliability assessment, expert opinions are oftentimes elicited to cope with the issue of poor quantity of failure data. However, information from expert subjective judgments may exhibit imprecision and be elicited from multiple physical levels of a system. Moreover, the elicited information may be conflicting as experts own varying backgrounds of knowledge as well as differentiated cognitive levels, which, thereby, cannot reach a consistent reliability estimate. In this article, we aim at conducting the reliability assessment of multistate systems by fusing conflicting multisource imprecise information (MSII) from the consensus reaching perspective. We utilize an aggregation operator to fuse individual opinions into a collective opinion in the form of mass functions. Evidence distance is, then, adopted to quantify the dissimilarity between individual and collective opinions, and accordingly, a measurement of the average degree of consensus is proposed. In this way, the consensus reaching model is formulated by minimizing the total calibration of MSII with the constraint of a predetermined consensus threshold. The consensus reaching model is resolved by a feasibility-based particle swarm optimization algorithm. A numerical example, along with an application of control rod drive mechanism in nuclear reactors, is used for the demonstration of the effectiveness of the proposed method.

In the system reliability assessment by multisource information fusion, the various sources of information often display biases and may be conflicting with each other. Practical scenarios typically require a consensus on the reliability estimate, which indicates that the multisource information has to be properly refined. This study introduces a consensus-reaching process aiming at calibrating imprecise information from diverse experts' opinions for multistate systems. Specifically, two interactive consensus reaching models, i.e., interactive minimum-cost reliability consensus model and interactive maximum consensus degree model, are put forth to allow experts to make cost-effective preference modifications to reach a reliability consensus. The interactive consensus reaching models use the evidential network and evidential utility function to amalgamate multisource imprecise information to reach a nominal reliability consensus. A feedback mechanism based on the belief Jensen–Shannon divergence measure is, therefore, developed to foster interaction between the expert's imprecise information and the nominal reliability consensus. Through the interactive consensus reaching process, the unified reliability estimate is assessed via a feasibility-based particle swarm optimization. The effectiveness of the proposed method is demonstrated via a numerical example and a control rod drive mechanism in nuclear power plants.

The Internet of Things (IoT) represents a transformative convergence of traditional manufacturing systems with advanced information technologies, collectively referred to as smart manufacturing. The interconnected nature of IoT facilitates real-time data collection and analysis, optimizing production processes and improving operational efficiency. However, the increased complexity and interdependence of IoT systems pose significant challenges in reliability modeling and assessment. This article introduces a novel reliability model that comprehensively integrates factors such as degradation of physical systems and information networks, along with their interactive impacts on system performance and reliability. A modular Petri net approach is developed to efficiently assess reliability of IoT systems by leveraging a structured framework to model the intricate interdependencies within IoT. The modular nature of the proposed approach enables targeted analysis and scalability enhancements, addressing the critical need for models that can adapt to the evolving landscape of IoT in smart manufacturing systems. A vehicle manufacturing system example is introduced to demonstrate the proposed approach. The results reveal the distinct impact pathways of the physical system and information network on overall system reliability. Statistical analysis across various system configurations shows that modifying the architecture of the information network can lead to an average improvement of 20.67% in system reliability.

Engineered systems are increasingly integrating sensor techniques to trace their specific degradation behaviors, so as to facilitate their dynamic reliability assessment. Due to the hierarchical structure of these systems, sensing data can be collected at multiple physical levels, including the entire system, subsystems, and components. The quality of collected multilevel sensing data, however, decreases inevitably with the degradation of sensors mounted within each system, leading to a declining trustworthiness of dynamic reliability assessment for each specific individual system. This article develops a new dynamic reliability assessment framework of hierarchical multistate systems suffering from sensors’ degradation. The proposed framework mainly contains three steps: 1) utilizing discrete-state and continuous-state stochastic processes to, respectively, model the degradation behaviors of two types of sensors; 2) integrating these two types of sensors’ degradation models to update the joint state probability distribution of both the monitored objects and sensors by fusing multilevel sensing data; 3) deriving the marginal state probability distribution of the entire system to dynamically assess system reliability. A three-component system and an electromechanical actuator system in landing gear systems are exemplified to illustrate the performance of the proposed method.

Selective maintenance, as a prevalent maintenance policy for engineered systems under limited maintenance resources, has been widely adopted in industrial and military settings. Most existing works on selective maintenance only considered limited consumable resources, such as time and budget. In many real-world applications, the implementation of maintenance activities, however, has to be supported by several maintenance capacities, including repairpersons and repair facilities, which are occupied during the execution of a maintenance action and released upon its completion. Moreover, due to the stochasticity of maintenance actions’ durations, the available number of maintenance capacities in each period is also uncertain. In this article, a novel dynamic selective maintenance model is introduced by taking account of the limited maintenance capacities and stochastic action durations. The dynamic optimization problem is formulated as a Markov decision process where maintenance actions are dynamically selected in accordance with components’ states, remaining consumable resources, and available maintenance capacities. An approximate dynamic programming algorithm based on the rollout policy is put forth to estimate the optimal selective maintenance policy, and an importance-based heuristic is proposed to enhance its performance. To overcome the inefficiency of the solution algorithm in coping with large-scale instances, a machine learning-enhanced framework that enables neural networks trained by small-scale instances to solve large-scale instances is developed. A manufacturing system and an aircraft fleet are exemplified to demonstrate the effectiveness of the proposed approach.

Thek-out-of-nsystem with functional dependency (FDEP), as a typical structure, has widespread applications in a diversity of engineered system. These systems are characterized by components that perform distinct functions, and are connected through flexible intercomponential support relations. This flexibility allows for dynamic adjustment of the support strategy in response to component failures, achieved through connections between components’ interfaces or controlled by additional components, such as valves and switches. Even though previous article has demonstrated effectiveness in assessing reliability ofk-out-of-nsystems with FDEP, it often overlooks the essential investigation of flexible support relations among components, resulting in inaccurate system reliability assessment. To fill this research gap, this article introduces a novel framework that integrates a parameter time-varying discrete dynamic Bayesian network (PTVDDBN) and a tailored Hungarian algorithm with a depth-first search (DFS) strategy, namely the PTVDDBN–HDFS method, to advance reliability assessment ofk-out-of-nsystems with flexible support relations. Specifically, the PTVDDBN-based architecture captures the system's stochastic degradation over time, and its components’ lifetime could follow an arbitrary probability distribution. From a graph set-based perspective, the support strategy designated in the system is dynamically adjusted via the DFS strategy. The optimal system performance under various component state combinations is further converted to conditional probability table parameters within the PTVDDBN model. A practical case study of a kerosene filling system at a space launch site is showcased to illustrate the application and effectiveness of the PTVDDBN–HDFS method.

Power substations are widely used as crucial components of power grids but also exposed to a high risk of earthquakes. Enhancing the resilience of power substations plays an important role for power grids to resist earthquakes. However, the uncertainty of equipment failure has posed a significant obstacle to enhancing resilience. In this article, considering the equipment hardening strategy for the power substation, a two-stage distributionally robust optimization model is put forth for earthquake resilience enhancement of the power substations. The optimal equipment hardening strategy is determined prior to an earthquake, and the recovery sequence of the damaged equipment is optimized after the earthquake to enhance the resilience of the power substation. A decision-dependent moment-based ambiguity set is constructed to model the impact of the hardening strategy on the uncertain failure probability of equipment. A customized nested column-and-constraint generation algorithm (NC&CG) is put forth to solve the optimization model. To improve the computational efficiency, we propose a novel heuristic algorithm to solve the main problem of the inner NC&CG according to the power substation structure. The proposed method is demonstrated in the case of a simplified 220 kV power substation. The results show that the distributionally robust approach can effectively enhance the earthquake resilience of power infrastructure under uncertainty of equipment failure. The value of implementing an effective algorithm to quickly obtain the optimal solution in large-scale problems is also highlighted.

Integrated circuit (IC) marking inspection is a crucial task to ensure product quality in electronics manufacturing. Due to the diversity of marking appearance, high environmental complexity, and massive annotation costs, it is, however, still a great challenge to accurately recognize IC markings in a real-time fashion at some production stages, such as surface mount technology (SMT). In this article, an end-to-end deep learning model with three branches is put forth for IC marking inspection. The saliency activation branch provides powerful shared feature representation, and by incorporating with the weakly supervised mechanism, it can generate precise character localization information with coarse-grained annotation. The direction recognition and character recognition branches utilize shared saliency maps to sample word-level and character-level features, respectively, such that the network can properly recognize markings in different orientations, and especially perform well on the chips with multidirectional markings. The proposed character box refinement method allows the network to adapt to tiny size and tight-layout IC markings, and a new loss function called ED-Loss is designed for error estimation between the unaligned sequences. Experiments on a real SMT chip dataset with highly diverse IC images show that the model reaches a recall rate of 96.34%, with an inspection speed close to 30 fps. The comparative experiments with the state-of-the-art models demonstrate that our model has superior performances in terms of accuracy, efficiency, and adaptability.

Defect detection tasks of solid propellants (SPs), involving size, shape, and surface defects, are essential for ensuring the quality of many industrial products. Developing separate models for three tasks, however, is complicated and inefficient due to the redundant deployment. Multitask learning (MTL), with its potential for knowledge sharing, may greatly reduce the space and power consumption, but still faces the challenges of destructive interference and empirical tradeoffs between tasks. To this end, a novel end-to-end network for multidefect detection of SPs is put forth: 1) a new setting for MTL without any empirical tradeoffs is introduced, in which the knowledge is shared while the models are not visible to each other among diverse tasks; 2) in this setting, a bilateral feature extractor is constructed to extract both low- and high-level features, and a feature fusion module is further exploited to encourage each task to adaptively learn the task-specific knowledge; 3) an end-to-end training manner with a dynamic balance strategy and a gradient stop-flow strategy is designed to ensure that different tasks can benefit from, but do not interfere with, each other; 4) the introduction of semantic knowledge from the size detection branch enables the surface detection branch to learn semantic features beyond only pixel-to-pixel mapping. A smoothness construction loss is further designed to boost the performance of the surface detection task. Experimental results on an image dataset from a real-world manufacturing line show that the setting for MTL has the superiority in terms of the model size, inference speed, and detection accuracy.

Frequent and sizable voltage fluctuation, a common issue faced by the modern distribution system (DS), could lead to potential equipment failures and power interruption. This brings huge negative impact on the power supply reliability of the DS. Existing voltage regulation methods typically rely on the precise physical parameters, complete measurements, and perfect communication, all of these premises are difficult to meet in practice. To this end, a decentralized control method that is robust to measurement acquisition errors is developed for DS in this article. Specifically, a graph learning-based surrogate network is first built to simulate the power flow computing procedure and capture the structural characteristics of the DS. The centralized surrogate model is, then, divided into several decentralized representation networks according to the network partition results to obtain the robust embedding of the regional information of each subnetwork. Subsequently, the representation networks are embedded in the front of the actor networks of the multi-agent soft actor-critic algorithm, the agents of which are learned in a centralized fashion according to the reward value estimated by the centralized surrogate model. The systematic integration of the three components allows us to achieve cooperation between different subregions and robustness against anomalous measurements without the reliance on precise circuit parameters. Comparative studies on IEEE test system illustrate the robustness of the proposed approach.

Deep learning methods have received tremendous attention in remaining useful life (RUL) prediction in recent years. Despite the promising results achieved by those deep learning methods, they failed to take account of the impact of varying future operations on RUL prediction and prognostics uncertainty. In most industrial scenarios, the RUL of products is closely related to future missions and loading profiles, and they ought to be considered for RUL prediction. In addition, Bayesian deep learning treats the model parameters as random variables, and takes advantage of the Bayesian formulas for adaptive model parameter updating to obtain credible intervals of RUL prediction. In this article, a Bayesian dual-input-channel long short-term memory (BDIC-LSTM) network is put forth to conduct the point estimation and credible interval estimation of RUL prediction. The BDIC-LSTM network consists of a DIC-LSTM network and an improved Monte Carlo dropout (IMCD) method to effectively extract the features of future operations and quantify the prognostics uncertainty, respectively. In the DIC-LSTM network, the raw signal data are fed into the main input channel consisting of LSTM modules. Meanwhile, bidirectional LSTM (Bi-LSTM) modules are leveraged as an auxiliary input channel to fully extract the future operation information in the operation data. The IMCD method is investigated to estimate the credible intervals of RUL via decomposing the prognostics uncertainty into aleatory uncertainty of measurement data and epistemic uncertainty of the network. For the training of the BDIC-LSTM network, a padding and packing training mode, an improved loss function, together with a Lookahead optimizer, are devised to accelerate the convergence speed and enhance the accuracy of prognostics. Experiments on the C-MAPSS dataset are carried out to validate the effectiveness of the proposed method.

Inspection is a crucial activity for an engineered system as its results can reduce the uncertainty of identifying the true states of the system and its components, so as to facilitate subsequent proactive maintenance. The preliminary work to conduct an inspection activity is to evaluate its effectiveness. In many real-world scenarios, engineered systems oftentimes possess both multistate and hierarchical characteristics, and inspection can be performed across multiple physical levels of a system. We, therefore, need a measure to assess the effectiveness of a multilevel inspection activity of multistate systems. Inspired by the concept of importance measure, in this article, we define a new measure, namely, inspection importance measure (InsIM), to assess the contribution of a multilevel inspection strategy to the efficiency improvement of the subsequent preventive maintenance from a value of information perspective. The proposed measure evaluates the increased efficiency of preventive maintenance after conducting multilevel inspection activities. The procedure of the proposed InsIM contains four steps: 1) calculating the efficiency of the optimal maintenance policy identified without inspections, 2) updating the system's state distribution by multilevel inspection activities, 3) calculating the efficiency of the optimal maintenance policy identified with inspections, and 4) evaluating the expected improvement of maintenance policy. A five-component system and a real-world programmable logic controller control system are exemplified to demonstrate the accuracy and effectiveness of the proposed method. The results indicate that the InsIM can significantly enhance the efficiency of the subsequent proactive maintenance decision.

Reducing vulnerability and enhancing resilience of infrastructure networks subject to uncertain disruptions is a challenging task as these networks become increasingly interconnected and interdependent. This article devotes to addressing the preparedness planning problem of interdependent infrastructure networks. The interdependency between infrastructure networks is characterized by a two-way physical interdependency, that is, the state of one infrastructure network is dependent on that of another infrastructure network, and vice versa. Furthermore, the multistate characteristics of infrastructure networks are taken into account and accommodated to the studied physical interdependency. A tailored two-stage stochastic programming framework, which is able to cope with the uncertainty associated with disruption scenarios, is put forth to facilitate an effective resilience enhancement strategy under a limited budget. In this framework, the first-stage problem selects the optimal protection levels of network components in advance, whereas the second-stage problem optimizes the network operation after a disruption scenario occurs. The proposed framework is implemented to an illustrative system composed of interdependent power–water distribution networks to demonstrate the effectiveness of the resilience enhancement strategy.

Expert knowledge is an important information source for system reliability assessment, especially when historical data are limited. However, when elicited, expert knowledge is often imprecise with large uncertainty. Moreover, as experts usually own different expertise and knowledge, the elicited knowledge from different experts might be conflicting. In this article, a two-stage optimization model is put forth to fuse the imprecise and conflicting information from multiple sources to assess reliability of multistate systems. The degradation of the components in the multistate system is modeled via imprecise Markov models. Then, in the first-stage optimization, upper and lower bounds of the degradation model parameters are determined by minimizing the conflict between the prediction of the model and the multisource imprecise information elicited from experts. A particle swarm optimization algorithm is tailored to solve the computational problems brought by the presence of high-dimensional decision variables and resolve the optimization problem. The second-stage optimization is, then, conducted to identify the upper and lower bounds of the system reliability function given that the degradation model parameters are constrained in the bounds obtained from the first-stage optimization. A numerical example, along with a radar display and control system, is used to demonstrate the effectiveness and applicability of the proposed method.

Fast recognition of integrated circuit (IC) markings is an essential but challenging task in electronic device manufacturing lines. This article develops an adaptive deep learning framework to facilitate the fast marking recognition of IC chips. The proposed framework contains four deep learning components, namely, chip segmentation, orientation correction, character extraction, and character recognition. The four components utilize different convolutional neural network structures to guarantee excellent adaptivity to a wide range of IC types and mitigate the influence of the low-quality chip images. In particular, the character extraction model is comprised of two improved label generation strategies and a proposed border correction method, so as to accommodate tiny scale chips and compactly printed markings. Experiments from the chip image dataset of a real laptop manufacturing line reached a recognition Precision of 91.73% and the Recall of 92.93%. The results demonstrate the superiority of the proposed framework to the state-of-the-art models and the effectiveness of handling a great diversity of chips with different scales, shapes, text fonts, marking colors, and layouts.

As multistate system (MSS) reliability models can characterize the multistate deteriorating nature of engineering systems, they have received considerable attention in the past decade. The states of a multistate system/component can be distinguished by its performance capacity, which deteriorates over time and can be restored by maintenance activities. On the other hand, the deterioration of a system/component is, oftentimes, controllable by setting a loading strategy. In this article, a dynamic load optimization problem for repairable MSSs is investigated to achieve the maximum expected cumulative performance within a finite time horizon and limited maintenance resources. The degraded components in a system are dynamically maintained to recover to their better conditions, whereas the performance rate of each component can also be dynamically specified. The resulting sequential decision problem is formulated as a Markov decision process with a continuous action space and a mixed integer discrete continuous state space. The deep deterministic policy gradient algorithm, which is a specific deep reinforcement learning algorithm in the actor−critic framework, is customized to overcome the “curse of dimensionality” and mitigate the uncountable state and action spaces. The effectiveness of the proposed method is examined by two illustrative examples, and a set of comparative studies are conducted to demonstrate the advantage of the proposed dynamic loading strategy.

In engineering scenarios, expert judgments play an essential role in reliability assessment, especially for those systems with few historical data. To achieve a rational result, experts from different areas should be involved, and the uncertainties in their assessments should be properly addressed. Such information is often referred to as multisource imprecise information (MSII) and might contain high degree of conflicts, as different experts usually have different expertise and knowledge. Properly quantifying the conflicts among the MSII, then, becomes a critical issue, as the subsequent processing of MSII (e.g., combination and calibration), depends on the degree of conflict in the MSII. To this end, a new conflict measure is put forth based on the Dempster–Shafer theory (DST) to quantify and visualize the conflict in the MSII from a group of experts. In the first place, the MSII from each expert is used to construct the basic belief assignment (BBA) of the reliability estimates for the corresponding expert under the DST. A 2-D conflict measure, which combines the conflict factor and Jousselme distance in DST, is, then, proposed to measure the conflict between the experts’ BBAs. The conflict is quantified from two perspectives, viz., mutual conflict and total conflict. Finally, a Bhattacharyya distance-based method is developed to further quantify the informativeness of each expert's MSII to the system reliability estimate. A numerical example along with an engineering case is used to validate the effectiveness of the proposed approach.

Improving reliability and eliminating the potential design risk are crucial for product design. Failure mode and effect analysis (FMEA), as an effective reliability assurance tool, has been extensively used in product design. However, causalities among failure modes, interactions among risk factors, and correlations among risk evaluations were not jointly considered in existing FMEA methods. On the other hand, the cost and time caused by the occurrence of failure modes were seldom incorporated into risk factors. Due to the lack of accurate values and/or information loss of customers and experts, these risk factors inevitably contain uncertainty that cannot be overlooked in product design. In this article, a novel FMEA-based approach is proposed to facilitate risk analysis of product design under uncertainty. In this approach, the stable grey causality vector state and the grey interaction vector are respectively established to characterize causalities and interactions. To reduce the uncertainty contained in cost and time, the extended information axiom is put forth, and then, their grey information contents can be obtained and are to be incorporated into the design. Subsequently, we extend Choquet integral to prioritize the potential failure modes and identify the optimal design scheme while coping with correlations. The proposed approach is validated by an example of a substrate design.

In this article, we develop a mixture of Gaussians-evidential hidden Markov model (MoG-EHMM) to fuse expert knowledge and condition monitoring information for remaining useful life (RUL) prediction under the belief function theory framework. The evidential expectation-maximization algorithm is implemented in the offline phase to train the MoG-EHMM based on historical data. In the online phase, the trained model is used to recursively update the health state and reliability of a particular individual system. The predicted RUL is, then, represented in the form of its probability mass function. A numerical metric is defined based on the Bhattacharyya distance to measure the RUL prediction accuracy of the developed methods. We applied the developed methods on a simulation experiment and a real-world dataset from a bearing degradation test. The results demonstrate that despite imprecisions in expert knowledge, the performance of RUL prediction can be substantially improved by fusing expert knowledge with condition monitoring information.

The reliability function of a specific individual system can be dynamically updated by utilizing inspection data collected over time. However, due to limited inspection resources, such as time, budget, and manpower, it is oftentimes impossible to collect all the inspection data for all the components, subsystems, and the entire system simultaneously. There is an urgent need to optimally allot the limited inspection resources across multiple physical levels of a system, so as to identify the health status of a system and/or its subset of components of interest as accurately as possible to facilitate the ensuing system health management. To address the above research question, a metric is put forth in this paper to quantify the effectiveness of a particular multilevel inspection strategy for multistate systems (MSSs). Based on the proposed metric, an optimization problem is formulated to seek the optimal multilevel inspection strategy which possesses the maximum effectiveness of revealing the true state of a system and/or its subset of components of interest under limited inspection resources. The resulting optimization problem is resolved by a tailored ant colony optimization algorithm. The findings from our illustrative examples are 1) the proposed metric is capable of quantifying the effectiveness of various multilevel inspection strategies; 2) the analytical solution of the proposed metric is exactly the same with the simulation results, but much more computationally efficient; and 3) the optimal inspection strategy varies with respect to the operation time of a specific individual system.

Traditional time-based reliability assessment methods compute reliability measures of a multistate system (MSS) purely based upon historical time-to-failure data collected from a large population of identical systems. Using these methods, one can only assess the reliability of a system from a population or statistical perspective. Moreover, these methods fail to characterize the stochastic behavior of a specific individual MSS over time. Accordingly, in this paper, a dynamic reliability assessment method that can aggregate inspection data across multiple levels (such as component level, subsystem level, and system level) of a nonrepairable MSS has been studied. In general, inspection data collected from multiple levels of a system can be imperfect, but they are stochastically correlated with the actual states of the inspected system and components. A set of two-stage recursive Bayesian formulations has been put forth to dynamically update the reliability function of a specific MSS over time by utilizing imperfect inspection data collected simultaneously or asynchronously from multiple levels of the system. The proposed method is exemplified via an illustrative example of an underground flow transmission system. The impact of the probability of detection on the accuracy of the remaining useful life prediction is also examined.

This paper develops a Bayesian framework to assess the reliability and performance of multi-state systems (MSSs). An MSS consists of multiple multi-state components of which the degradation follows a Markov process. Due to the lack of sufficient data, and only vague knowledge from experts, the transition intensities of multi-state components between any pair of states and the state probabilities cannot be precisely estimated. The proposed Bayesian method can merge prior knowledge from experts' judgments with continuous and discontinuous inspection data to obtain posterior distributions of transition intensities. A simulation method embedded with the universal generating function (UGF) is developed to estimate the posterior state probabilities, the reliability, and the performance of the entire MSS. Two numerical experiments are presented to demonstrate the effectiveness of the proposed method.

Traditional time-based reliability assessment methods evaluate the reliability of a multi-state system (MSS) from a population or a statistical perspective that the reliability of a system is computed purely based upon historical time-to-failure data collected from a large population of identical components or systems. These methods, however, fail to characterize the stochastic behaviors of a specific individual system. In this paper, by utilizing system-level observation history, a dynamic reliability assessment method for MSSs is put forth. The proposed recursive Bayesian formula is able to dynamically update the reliability function of a specific MSS over time by incorporating system-level inspection data. The dynamic reliability function, state probabilities, and remaining useful life distribution of an MSS in residual lifetime are derived for two common cases: the degradation of components follows a homogeneous continuous time Markov process, and a non-homogeneous continuous time Markov process. The effectiveness and accuracy of the proposed method are demonstrated via two numerical examples.

Because of the complexity of engineering systems, and the fact that insufficient data are only available to obtain the precise state probability of components, an extended universal generating function (UGF) based on belief function theory is introduced in this paper to conduct the reliability analysis of multi-state systems (MSSs) with epistemic uncertainty. The behavior of common cause failures (CCFs) is further incorporated, and the occurrence probability of CCFs is evaluated using a weighted impact vector method. A numerical example is used to illustrate how the proposed method works. In addition, a global optimization method is used to obtain the truth interval of the system reliability, and the results are compared with those obtained by using some existing methods. The case study shows that the belief UGF method can effectively avoid the interval expansion problem and the overestimation problem involved in the interval UGF method, and the proposed method can be used to provide a reliable way to evaluate the reliability of MSSs with interval data and CCFs.

The redundancy allocation problem has been extensively studied with the aim of determining optimal redundancy levels of components at various stages to achieve the required system reliability or availability. In most existing studies, failed elements are assumed to be as good as new after repair, from a failure perspective. Due to deterioration, the repaired element cannot always be restored to a virtually new condition unless replaced with a new element. In this paper, we present an approach of joint redundancy and imperfect maintenance strategy optimization for multi-state systems. Along with determining the optimal redundancy levels, the element replacement strategy under imperfect repair is also optimized simultaneously, so as to reach the desired availability with minimal average expenditure. A generalized imperfect repair model is proposed to characterize the stochastic behavior of multi-state elements (MSEs) after repair, and a replacement policy under which a MSE is replaced once it reaches the pre-determined number of failures is introduced. The cost-repair efficiency relation, which regards the imperfect repair efficiency as a function of assigned repair cost, is put forth to provide a flexibility of assigning repair efforts strategically among MSEs. The benefits of the proposed method compared to the existing ones are demonstrated and verified via an illustrative case study of a three-stage coal transportation system.

Reliability analysis of complex systems is a critical issue in reliability engineering. Motivated by practical needs, this paper investigates a Bayesian approach for system reliability assessment and prediction with multilevel heterogeneous data sets. Two major imperatives have been handled in the proposed approach, which provides a comprehensive Bayesian framework for the integration of multilevel heterogeneous data sets. In particular, the pass-fail data, lifetime data, and degradation data at different system levels are combined coherently for system reliability analysis. This approach goes beyond the alternatives that deal with solely multilevel pass-fail or lifetime data, and presents a more practical tool for real engineering applications. In addition, the indices for reliability assessment and prediction are constructed coherently within the proposed Bayesian framework. It gives rise to a natural manner of incorporating this approach into a decision-making procedure for system operation and management. The effectiveness of the proposed approach is illustrated with reliability analysis of a navigation satellite.

Many imperfect maintenance models have been developed to mathematically characterize the efficiency of maintenance activity from various points of view. However, the adequacy of an imperfect maintenance model must be validated before it is used in decision making. The most adequate imperfect maintenance model among the candidates to facilitate decision making is also desired.

Many systems are required to perform a series of missions with finite breaks between any two consecutive missions. In such a case, one of the most widely used maintenance policies is a selective maintenance in which a subset of feasible maintenance actions is chosen to be performed with the aim at achieving the subsequent mission success under limited maintenance resources. Traditional selective maintenance optimization reported in the literature only focuses on binary state systems. Most systems in industrial applications, however, have more than two states in the deterioration process. In this work, a selective maintenance policy for multi-state systems (MSS) consisting of binary state elements is investigated. Taking the imperfect maintenance quality into consideration, the Kijima model is reviewed, and a cost-maintenance quality relationship which considers the age reduction factor as a function in terms of maintenance cost is established. Moreover, with the assistance of the universal generating function (UGF) method, the probability of the repaired MSS successfully completing the subsequent mission is formulated. In place of enumerative methods, a genetic algorithm (GA) is employed to solve the complicated optimization problem where both multi-state systems, and imperfect maintenance models are taken into account. The effectiveness of the proposed method is demonstrated via a case study of a power station coal transportation system. Finally, a comparative analysis between the strategies with and without considering imperfect maintenance is conducted, and it is concluded that incorporating imperfect maintenance quality into selective maintenance achieves better outcomes.

A multi-state system (MSS) has more than two discrete states corresponding to different performance rates. Usually, MSS is viewed as in a failure state once its performance rate falls below user demand, and maintenance is carried out immediately. Generally, the repaired system cannot be regarded as good as new, and oftentimes the system restoration is stochastic. We introduce an optimal replacement policy for MSSs, called policyN. Under this policy, a MSS is replaced whenever its failure number reachesN. We assess the dynamic element state probabilities of each aging multi-state element (MSE) using a stochastic process model which is identified as a non-homogeneous continuous time Markov model (NHCTMM), and we evaluate the state distribution of the entire MSS via the combination of the stochastic process, and the universal generating function (UGF). To quantify the quality of imperfect maintenance, a quasi-renewal process is used to describe the stochastic behavior of each individual MSE after repair. Moreover, we derive an explicit expression of the long-run expected profit per unit time, and determine the optimal failure numberN*to replace the entire system. The proposed models are demonstrated via an illustrative case, followed by some comparative studies.