Tightly interdependent cyber and service networks in the Manufacturing Internet of Things (MIoT) drive cascading failures to propagate in intertwined horizontal (intra-layer) and vertical (cross-layer) directions, greatly complicating post-cascading-failure recovery decisions. To address limitations of existing approaches that neglect cross-layer dependencies and struggle to simultaneously handle heterogeneous load patterns and multiple failure states, this paper proposes a coordinated recovery framework for cyber-service-coupled MIoT, termed the coupled reinforcement learning (Coupled-RL) mechanism. Specifically, the Coupled-RL-based recovery method equips two layer-specific recovery agents for the cyber and service networks and a lightweight coordinator that orchestrates cross-layer decision-making. This coordinator is designed to avoid infeasible and globally suboptimal plans: its Feasibility Module (FM) shares the set of repaired nodes between layers and filters out actions that violate cross-layer prerequisites, while its Prediction Module (PM) exchanges per-state maximal target Q-values across layers—these values are used to construct a coupled return and inject cross-layer foresight into the Bellman update process of the agents. A weighted coupled return function and an alternating decision procedure further enable decentralized policy coordination. Extensive experiments demonstrate that the proposed recovery method effectively addresses the two-layer network coordination problem in MIoT during cascading failure recovery. Additionally, a comparative analysis between the proposed algorithm and existing ones is conducted to verify its superiority.

With the rapid advancement of cloud and edge computing, cloud–edge collaborative systems have been widely deployed in applications such as smart manufacturing and the Industrial Internet of Things (IIoT). These systems exhibit multi state operational behavior with task migration among nodes, and their reliability is jointly influenced by state lag effects and epistemic uncertainty. This research develops a reliability model of a multi-state performance sharing system with epistemic uncertainty. A discrete-state continuous-time (DSCT) Markov process is employed to characterize component degradation, and a time-lag threshold interval is introduced to represent lag dependence in component states. Based on the Evidential Network (EN), a reliability assessment algorithm of a multi-state performance sharing system with time-lag dependence under epistemic uncertainty is proposed. Numerical results show that the common bus capacity has a significant effect on system reliability. The epistemic uncertainty of lag dependence impacts the degree of uncertainty in system reliability, but the impact decreases over time.

Intelligent manufacturing systems progressively advance toward highly collaborative and distributed decision making. Federated learning (FL)-enabled intelligent manufacturing systems facilitate efficient data processing and intelligent decision making by deploying artificial intelligence models at the edge and integrating model aggregation mechanisms. However, anomalies occurring in the local devices on which the local models depend can propagate through the aggregation process, leading to model contamination and performance degradation, thereby compromising the task reliability of the entire system. To address this issue, this article proposes a reliability modeling approach for FL-enabled intelligent manufacturing systems (FL-IMSs). In the proposed model, we characterize the performance degradation process of the local model caused by terminal device failures and its impact on task reliability. This process includes the effect of data quality degradation triggered by device failures on model performance, as well as failure propagation caused by intermodel dependencies. Furthermore, to assess the impact of model performance variations on practical production tasks, a task-oriented reliability metric is introduced. Simulation and experimental results demonstrate that the proposed modeling approach effectively captures local model performance degradation and task reliability in FL-IMSs under terminal device failure conditions.

With the advancement of digitalization and intelligentization in manufacturing systems, digital twin-driven cyber-physical manufacturing systems (DT-driven CPMSs) have emerged as a key technology for enabling smart manufacturing. Existing studies have primarily focused on the applications of DT technology, but have not fully addressed the reliability challenges arising from equipment degradation and sudden failures during system operation. To address this challenge, we propose an interdependent network model for DT-driven CPMSs that integrates real-time sensing and control feedback dependencies across the cyber layer, physical layer, and virtual decision space. The model emphasizes the characterization of data dependencies between devices under sensing-control dependencies, including production data support and collaborative production dependencies. Based on the proposed system model, we further develop a system reliability model. By incorporating the routing-driven characteristics of data in the cyber layer and the material supply-demand relationships among equipment in the physical layer, the proposed reliability model enables the joint modeling of long-term equipment degradation and sudden failure propagation under sensing-control dependencies within the system. Experimental results demonstrate that the proposed model can effectively capture system reliability behavior under these challenging operational conditions. Further analysis reveals that although the cyber layer constitutes a key bottleneck for system reliability, the physical layer is more effective in regulating it. Specifically, the average gain in system reliability achieved through redundancy enhancement in the physical layer reaches 0.82, which is significantly higher than the 0.39 gain achieved in the cyber layer.

Condition-based maintenance (CBM) powered by inspection/monitoring technology is crucial to guarantee safety and economical operations of various industrial assets. The implementation of prevailing CBM procedures for large-scale heterogeneous systems, however, is increasingly challenged by model intractability and computational cost stemming from the synergistic effect of information completeness and structure complexity. In this article, we innovatively devises a tractable CBM model for multicomponent continuously degrading systems under nonperfect inspection information, which is applicable to heterogeneous system structure and arbitrary hierarchical maintenance actions. The maintenance optimization problem of interest constitutes a continuous-state partially observable Markov-decision process applicable to heterogeneous system structures. A series of structure properties associated with systematic conditional reliability and accessibility of optimal solution are established, following which a multiagent reinforcement learning model governed by partial-independent parameter-sharing mechanism is employed to allow for solution search under continuous state–action space. A customized proximal policy algorithm is then leveraged to facilitate efficient agent training by diminishing the cure of dimension. Comparative experiments conducted on train wheel treads verify the superior model performance over cost control and computational efficiency improvement.

Inspection errors are extensively reported in equipment health management due to multisource noises and technical limitations, particularly in hidden defect diagnosis of the multistage failure process. This article proposes a state-age-dependent maintenance and spare control strategy to compensate inspection-error-induced risk (attributed to both false positive and false negative) during defect identification. Specifically, a dual-phase adaptive inspection accommodating health variation is scheduled, following which both spare ordering and replacement are postponed to compensate implication of false-positive error. In addition, age-based replacement supported by preponed standard ordering is implemented promptly to alleviate false-negative error impact. To mitigate downtime losses, a dynamic selection mechanism upon failure occurrence between urgent and standard orderings is executed. The long-run operational cost rate is minimized by the joint optimization of postponed intervals of ordering and replacement, as well as the second-phase inspection interval. The model applicability is demonstrated through numerical experiments conducted on high-speed train bogie bearings.

Cascading failures are a critical factor affecting the reliability of industrial Internet of things (IIoT) systems. Establishing a realistic cascading failure model is of significant importance for researching and improving the reliability of IIoT. However, existing research on cascading failure modeling for IIoT lacks in-depth exploration of the actual characteristics of industrial scenarios, making it difficult to accurately characterize the cascading failure process in IIoT. In this work, based on the cyber–service coupling characteristic of IIoT systems, we establish a realistic interdependent network model, taking into full consideration the sensing-control data flow, the service community structure, and the diverse coupling patterns. On this basis, a cascading failure model for IIoT is developed, considering the routing-driven characteristic of the cyber network and the production–supply relationships among various manufacturing units in the service network. Extensive experiments are conducted to verify the rationality of the proposed model, and some meaningful findings are also obtained.

Reliability evaluation of complex network is one of main topics in complex engineering systems, especially for Internet of Things (IoT). The reliability of IoT partially depends on its large-scale network. Especially, the lifetime distribution of large-scale network is critical for its health management. However, the large scale of the network usually leads to an expensive simulation time cost. Instead of direct simulation, we propose a method to infer the large-scale network lifetime using small-scale networks with the universal scaling function. We first find the scaling relationships between network lifetime and network size in a network model with failure coupling for two-dimensional square lattice network and Cayley tree network. Network lifetime with different size can be described by one universal scaling function. Then we perform theoretical analysis to derive the scaling relationships. Finally we apply these scaling relationships to wireless sensor network with coupled failures in more realistic situation as case study. From the simulation results of smaller-scale networks, we can infer the lifetime distribution of large-scale networks based on universal scaling function. The computation time and accuracy are compared with standard Monte Carlo simulation which shows that our method is faster and accurate. Our research shows that the proposed method using universal scaling functions can help us to infer the lifetime properties of large-scale networks with low computational cost. Our method can help fast reliability evaluations of large-scale complex networks with high accuracy.

Many production systems undergo a multistate deterioration process before failure, during which inspection and repair are used to detect and remove the defects. Given the limitations of technology and random noise, inspection and repair are always imperfect. This study considered imperfect inspection and repair for a system subject to a three-stage degradation process. The concepts of virtual age and the improvement factor were adopted to characterize the imperfect repair effect. To verify the effectiveness of the proposed model, we applied it to the case of a steel converter plant and used the genetic algorithm to search for the optimal solution. The numerical results indicated that an optimal arrangement of inspection policy could significantly reduce maintenance costs.

Condition-based maintenance (CBM), as a key component of asset health management, is crucial to enhance the operational safety and availability of diverse mechatronic systems, such as railway vehicles, wind power equipment, nuclear devices, etc. A common phenomenon observed in CBM is the existence of dispersibility regarding degradation-induced failure threshold, which affects the precision of maintenance decisions. This article addresses such challenges by scheduling a prognosis-centered intelligent CBM policy, which harnesses dynamic lifetime information to support both scheduled and opportunistic maintenance decision-making. The degradation is characterized by a generalized-form stochastic process, and the lifetime distribution is assessed through the fusion of multiple uncertainties. A dynamic reliability criterion is set to determine whether and when to postpone maintenance, whose interval is controlled by the remaining lifetime as well as an optimizable safety coefficient. The postponement interval, in turn, enables the planning of opportunistic maintenance to mitigate system downtime. The operational cost rate is minimized through the joint optimization of the inspection interval, conditional reliability threshold, and safety coefficient. The superiorities of the proposed policy over some conventional/heuristic maintenance policies are demonstrated by a case study on filed maintenance planning of high-speed train bearing.

Inspection is usually carried out periodically to update a system state such that the optimal maintenance policy can be determined. In order to obtain the best inspection and maintenance policy, existing research is focused on improving the modeling accuracy of the system failure process. Little work has been devoted to making full use of the system idle time, which is known as the production wait in production systems. In this research, the failure process of a single-unit system is modeled in three stages with consideration of its production wait time. The objective of minimizing the long-run average maintenance cost per unit time is achieved by finding the optimal length of the periodic inspection interval and renewal age for this single-unit system. By comparing this model with two two-stage inspection models, the numerical study of a real steelmaking converter confirms both the accuracy and effectiveness of the proposed inspection and maintenance model. Furthermore, the sensitivity analysis of different parameters is conducted to explore the optimal choice of maintenance strategy for different cost parameters and degradation parameters. The analysis provides useful management insights for decision-makers.

With the emergence of the industrial internet of things, distributed data storage systems have become widely used to store the monitoring data of power generation systems. Malicious hackers often try to destroy or steal these confidential data by illegally invading the systems. In addition to hackers’ illegal intrusions, the availability of the data stored is also affected by the internal failures of the system.In this research, two reliability models are formulated to study the reliability of a phased-mission distributed data storage system considering internal failures and illegal intrusion. The first model considers internal failures and data destruction, whereas the second model further considers data theft. Furthermore, the allocation of the data partitions is optimized so that system reliability can be maximized. Numerical experiments demonstrate the effectiveness of the proposed models and algorithms.

The sustainability of an open source project is essential for the long-term and reliable development of software. Most existing studies focus on the recommendation accuracy of bug report assignment while ignoring inexperienced developers in the open source community. This gives inexperienced developers less opportunity to resolve bugs and can cause them to gradually lose interest in the development of open source software (OSS). To address this problem, this article proposes a novel approach called sustainable recommender (SusRec) to make sustainable report assignments without sacrificing accuracy. The SusRec approach is based on multimodal learning and ensemble learning, and it consists of two stages: the preprocessing stage and the developer scoring stage. In the preprocessing stage, the approach selects candidate developers who have participated in the resolution of bugs under the product of a new bug report. It then divides the candidate developers into three types—core developers, active developers, and peripheral developers—according to their experience. In the developer scoring stage, multimodal learning is adopted to score the three types of bug report–developer pairs, and ensemble learning is adopted to weight the scores of the three types of bug report–developer pairs and recommend developers for bug reports. We conduct extensive experiments using the bug repositories of the Eclipse and Mozilla projects to compare the proposed SusRec approach with the baseline methods in bug report assignment. The results demonstrate that the proposed SusRec approach cannot only improve the accuracy of developer recommendations for bug reports, but also the sustainability of OSS projects by providing more opportunities for active developers and peripheral developers to participate in bug resolution.

Existing research has been concentrated on improving the reliability of a distributed computing system through optimizing tasks allocation, providing software redundancy and providing hardware redundancy. None of these works considered the performance sharing mechanism in a distributed computing system. Different from other performance sharing systems whose reliability can be calculated directly, the reliability evaluation of a distributed computing system with performance sharing is more challenging since the reliability depends on the task execution time of each processor after performance sharing. This research considers a distributed computing system with performance sharing mechanism such that the computing power can be redistributed among different processors in the system. A reliability model is proposed to evaluate the distributed computing system with performance sharing. An optimization model is formulated to derive the optimal performance sharing policy such that the system reliability can be maximized. Both analytic examples and numerical examples are carried out to illustrate the proposed model and algorithm.

Linear multistate consecutively connected systems (LMCCSs) have been widely applied in telecommunications. An LMCCS usually has several nodes arranged in sequence along a line, where connecting elements (CEs) are deployed at each node to provide connections to the following nodes. Many researchers have studied the reliability modeling and optimization of LMCCSs. However, most of the existing works on LMCCSs have focused on the uncertainty in connection ranges of CEs; none of them have considered signal loss during the transmission. In practice, a signal emitted from a node may neither completely reach nor completely not reach the destination node. In other words, only a fraction of the signal may reach the destination node whereas the rest is lost. This article makes new contributions by proposing a model that evaluates the expected signal fraction receivable by the sink node in an LMCCS subject to signal loss. Moreover, we solve the optimal design policy problem, which co-determines CEs allocation and nodes building to minimize the system cost while meeting certain constraints on system reliability and expected receivable signal fraction. Three examples are provided to illustrate the proposed model.

Multistate series-parallel system (MSSPS) is a widely used model for representing engineering systems, whose reliability has been extensively analyzed. Universal generating function (UGF) is an efficient method for evaluating the reliability of MSSPS. However, when facing the large-scale MSSPS, where the number of system components and possible states are enormous, calclating the exact system reliability can be rather time-consuming. To evaluate the reliability of large-scale MSSPS more efficiently, this paper proposes an approximation method, named continuization discretization approximation (CDA) method. The CDA approach consists of continuization and discretization processes. The continuization process applies Gaussian approximation method based on the central limit theory and the UGF technique to evaluate parallel subsystems. While the discretization process discretizes the continuous distribution to a discrete one, and proposes an algorithm to evaluate the series subsystems efficiently. The efficiency and accuracy performance of the CDA method can be adjusted by parameters according to the computational resource and the system scale. The newly proposed method is compared to the existing methods in evaluating the large-scale MSSPS. Numerical examples show that the CDA method has evident advantage in computational efficiency with satisfactory accuracy performance.

This paper studies the defense strategy for a parallel system subject to an unintentional impact and an intentional impact. Existing research assumes that system damage is caused by either natural disasters (unintentional impacts) or strategic attackers (intentional impacts). However, in practice, the defender may encounter diverse scenarios, where these two kinds of impacts can happen in a sequential order. Without knowing the precise occurrence sequence, the defender must allocate its limited resources against two successive impacts. In each contest, the defender can construct redundant elements and protect them from damage, to minimize the expected loss from system destructions. Illustrative examples of the optimal strategy are presented in three cases: first, where the unintentional impact comes first; second, where the intentional impact comes first; and third, where the two impacts come in an uncertain order. Supplemental protection is considered in the model extension, where the defender can allocate additional protection resources to those elements that have survived after the first impact.

Linear consecutive-k-out-of-n systems are frequently used to model vacuum systems, telecommunication networks, oil pipeline systems, and the photographing of nuclear accelerators. Substantial research has been devoted to analyzing the reliability of such systems, using many different approaches and assumptions. Nevertheless, existing reliability formulas may not be suitable for all real systems. This paper therefore proposes a nonrecursive closed-form expression for a consecutive-k-out-of-n system that is made up of three types of nonidentical components. The corresponding dynamic survival function and mean time to failure are derived for the suggested system, and numerical experiments are carried out to illustrate its application.

Warm standby redundancy is a fault-tolerant technique balancing the low economical efficiency of hot standby and the long recovery time of cold standby. In this paper, motivated by practical engineering systems, a general demand-based warm standby system (DB-WSS) considering component degradation process is studied. A series of intermediate states exists between perfect functionality and complete failure because of degradation processes. A lot of existing analytical reliability assessment techniques are focused on conventional binary-state models or exponential state transition distributions for a system or its components. In this paper, a novel reliability evaluation approach based on the multistate decision diagram for DB-WSS is proposed. The proposed technique can handle arbitrary distributions of degradation processes for multistate components or systems. Moreover, considering the imperfect switch of the warm standby component, the start failure probability is taken into account in the warm standby system. Numerical studies are given to illustrate the proposed approach.

In this paper, we consider the replacement of a unit that is subject to a dominant failure mode. The unit is usually replaced by an age-based replacement policy, either when a preset age limit has been reached, or when failure occurs before this limit. However, the unit can also be replaced when it encounters a random production wait and its age has reached a certain threshold. Using such an opportunity for replacement can help to minimize system downtime. We formulate this joint age-based replacement limit and threshold optimization problem with the objective of minimizing the expected cost per unit time in the long run. A real-data example is presented to illustrate the applicability and effectiveness of our model.

To improve the system reliability while conserving the limited system resources, cold standby sparing is often used. In computing tasks, because active components fail randomly, and the standby component has to pick up the mission task whenever required, scheduled backups are often implemented to save the completed portions of the task. The backups can facilitate an effective system recovery where the standby component can take over the mission task from the last backup point instead of resuming the mission task from the very beginning. This paper considers a k-out-of- n cold standby system subject to scheduled backups, where k components are online and operating, with the remaining components waiting in the unpowered, cold standby mode. Whenever an online component fails, a cold standby component is activated to take over the mission task from the last backup point. The backup intervals are deterministic, but can be even or uneven. As the component may fail due to an imperfect switching from the standby state to the fully powered up state, the switching failure is also considered in the system model. A multi-valued decision diagram (MDD)-based analytical approach is proposed to evaluate the reliability of the considered system, and its complexity is analyzed. The proposed method is applicable to systems with non-identical components following arbitrary lifetime distributions. Examples are given to illustrate the MDD-based method. The correctness and efficiency of the proposed method are verified using Monte Carlo simulations.

Optimal component order can effectively improve the system reliability for the design of a warm standby sparing (WSP) system. The optimal component order in the 1-out-of- n WSP system is studied in this paper. The optimal component order strategies in terms of the expected system lifetime are proposed, and proved for several cases. Furthermore, the 1-out-of- n WSP system with exponential components is investigated from the viewpoint of the system reliability; it is proved that the components should be activated according to the descending order of their failure rates. These results are very useful and applicable in the design of 1-out-of- n WSP systems.