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.

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.

In the past decade, the sensor and surveillance technology have been widely used in condition monitoring. The hidden states of systems can be inferred from collected sensor data. However, the maintenance decision problem becomes more challenging when ordering decision of the spare parts must be considered jointly. In this article, we consider a multistate deteriorating system whose states are hidden but partially observable, and determine the optimal maintenance and spare parts inventory ordering policy. We use the partially observable Markov decision process to model the problem of interest and adopt the state-of-the-art heuristic search value iteration algorithm to solve the optimization problem. The proposed policy is illustrated and compared with$( {{\bm{s}},{\bm{S}}} )$inventory policy through a series of numerical examples. The numerical results indicate that our proposed policy is cost effective. Further, the model of multicomponent system is formulated, highlighting the adaptability of our framework. This research shows that considering the system component conditions and spare parts ordering jointly can result a lower operation and maintenance cost.

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.

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.

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.

In many real production systems, a system may be stopped due to a lack of demand or exhaustion of raw materials. This is known as production wait and provides a good opportunity for maintenance. Meanwhile, the increased complexity of the modern machines brings new challenges for modeling and analyzing their failure behaviors. To address these real-world problems, this article considers a single-unit system that may fail due to either hard failures or soft failures. The wait time of a system is utilized to conduct inspections and maintenance. The system is replaced when a defect is found during an inspection, a failure occurred or a prespecified age threshold is reached, whichever comes first. The cost model, which is the long-run maintenance cost per unit of time, is derived. The optimal periodical inspection interval and the threshold age to minimize the long run maintenance cost per unit of time is then obtained. A case study is conducted to demonstrate the proposed maintenance model. The study shows using the proposed maintenance model can reduce the cost. Sensitivity analysis illustrates how each cost parameter affects the optimal inspection interval and the optimal age threshold.

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.

Ranking and selection (R&S) procedures are powerful tools to enhance the efficiency of simulation-based optimization. In this paper, we consider the R&S problem subject to stochastic constraints and seek to improve the selection efficiency by incorporating the information from across the domain into quadratic regression metamodels. To better fulfill the quadratic assumption of the regression metamodel used in this paper, we divide the solution space into adjacent partitions such that the underlying functions of both the objective and constraint measures in each partition are approximately quadratic with homogeneous noise. Using the large deviations theory, we characterize the asymptotically optimal allocation rule by maximizing the rate at which the probability of false selection tends to zero. Numerical experiments demonstrate that our approach dramatically improves the selection efficiency by 50%-90% on some typical selection examples compared with the existing approaches.

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.

Ranking and selection procedures have been successfully applied to enhance the efficiency of simulation in recent years. To further improve the efficiency, one approach is to incorporate the simulation output from across the domain into some response surfaces. In this paper, the domain of interest is divided into adjacent partitions and a quadratic regression function is assumed for the mean of the underlying function in each partition. Using the large deviation theory, an asymptotically optimal allocation rule is proposed with the objective of maximizing the probability of correctly selecting the best design point. The proposed simulation budget allocation rule is implemented in a heuristic sequential allocation algorithm and compared with some existing allocation rules. Numerical results illustrate the effectiveness of the proposed simulation budget allocation rule.

Previous research in ranking and selection focused on selecting the best design and subset selection. Little research has been done for ranking all designs completely. Complete ranking has been applied to design of experiment, random number generator and population-based search algorithms. In this paper, we consider the problem of ranking all designs. Our objective is to develop an efficient simulation allocation procedure that maximizes the probability of correct ranking with fixed limited computing budget. A previous allocation strategy of complete ranking based on indifference zone formulation is conservative and not efficient enough. We use the optimal computing budget allocation framework to further enhance the efficiency and reduce the amount of budget needed to achieve the same probability of correct ranking. Compared with the previous allocation strategy, our proposed allocation rule performs best under different scenarios.