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Systems are damaged due to various disturbances, and the reliability of the systems is reduced. Measures to improve system resilience need to be studied since many systems still need to operate normally after suffering damage. In this paper, the whole process of the disturbance and recovery of the system is considered, and a resilience optimization model of a multi-component system is proposed. Firstly, a system resilience assessment method is proposed based on system reliability, and the system resilience loss is used as the resilience assessment index. Secondly, two component importance indexes, loss importance and recovery importance, are proposed for the system disturbance phase and recovery phase, respectively. The two importance indexes are weighted to obtain the weighted importance so as to measure the change law of system resilience and determine the influence degrees of components on system reliability. Then, under the constraint of maintenance time, an optimization model is established to determine a redundancy strategy to maximize system resilience. Finally, through an example analysis of a wind turbine system with its main components, it is verified that the redundancy strategy proposed with this method can reduce the loss of system resilience and effectively improve system reliability. [ABSTRACT FROM AUTHOR]

Urban road networks have promoted high-quality travel for residents by increasing connectivity and intelligence. But road congestion has not been effectively alleviated, causing a loss of time and energy. At present, the recovery of urban road networks mainly considers removing the failed edges. Considering the recovery cost and time, it is important to take active maintenance behavior to restore these networks. One of the key problems is dispatching traffic workers reasonably to achieve timely maintenance. In this paper, a flow-distribution-based process and execution (FD-PE) model is established for solving congestion. The maintenance centers (MC) study the reasons for and spread of congestion by edge flow. Based on the genetic algorithm (GA), two models of maintenance for urban road networks are developed, which include a single MC-centered dispatching plan and the co-scheduling of MCs. Both models aim at minimizing recovery time and allocating maintenance resources. The road network in Zhengzhou is borrowed as a case to explain the feasibility of the proposed models. The results show that on the premise of dividing network regions, it is reasonable to take a single MC to recover congestion. Compared with a single MC, the co-scheduling of MCs may save more time. [ABSTRACT FROM AUTHOR]

Wind farms have gained wide attention due to unlimited resources and clean energy. Considering that wind turbine systems are always in harsh conditions, subsystem failures could reduce the reliability of wind turbine systems. At present, the maintenance behaviors for wind turbine systems are various (e.g., corrective maintenance, preventive maintenance) when reliability is reduced below the threshold. Considering the maintenance cost and downtime, it is impossible to repair each component in a timely manner. One of the key problems is dividing components into maintenance groups to improve maintenance efficiency. In this paper, a grouping maintenance policy considering the variable cost (GMP-VC) is proposed to improve direct-drive permanent magnet (DPM) turbine systems. Grouping modes are proposed to fully consider the stated transition probability of turbine components and the variable cost of turbine systems. A maintenance model is formulated to select components as members of the group based on a RIM-VC index. An instance is given to verify the proposed GMP-VC method. The result indicates that the proposed maintenance policy may save maintenance costs over baseline plans. [ABSTRACT FROM AUTHOR]

Airbag systems are important to a car's safety protection system. To further improve the reliability of the system, this paper analyzes the failure mechanism of automotive airbag systems and establishes a dynamic fault tree model. The dynamic fault tree model is transformed into a continuous-time Bayesian network by introducing a unit step function and an impulse function, from which the failure probability of the system is calculated. Finally, the system reliability and average life are calculated and analyzed and compared with the sequential binary decision diagram method. The results show that the method can obtain more accurate system reliability and effectively identify the weak parts of the automotive airbag system, to a certain extent compensating for the lack of computational complexity of dynamic Bayesian networks in solving system reliability problems with continuous failure processes. [ABSTRACT FROM AUTHOR]

This paper divides the execution process of the command post system into four stages: information acquisition, information processing, decision control and response execution. It combines multilayer complex networks with a phased-mission system. Most studies have only evaluated the reliability of phased-mission systems. This paper evaluates and optimizes the reliability of a phased-mission system. In order to improve the mission success rate and maximize the reliability of a command post system, this paper provides a multitasking node criticality index, and the index is used to identify the key nodes in the command post's four-stage network Then, the hot backup system of the node is selected to determine the redundant structure of the key node. Under the constraints of the operation and maintenance costs of key nodes, with the goal of maximizing the reliability of the information processing network layer, the multitask redundancy optimization model of each stage is established. Finally, the reliability of the missions before and after redundancy optimization is compared, using the case analysis of the four-layer network to verify the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

The metro network plays a vital role in the urban transportation system. However, the metro network is easily damaged by humans and natural disturbances. This can cause serious economic damage, such as the suspension of metro station operations and line disruptions. Therefore, we conducted this study in order to minimize the loss caused by the damage to the metro network and improve the performance of the network after recovery. Based on the cascading failures of metro networks, this paper proposes a recovery model for metro networks considering the value of time. Then, considering the time value, a new node importance measure is proposed using the determination of maintenance priorities. The maintenance priorities of nodes with different importance values are investigated to minimize network losses. Lastly, the applicability of the method is verified by a metro network in Zhengzhou city. [ABSTRACT FROM AUTHOR]

• Analyze the phase performance characteristics of the urban sewage treatment system. • Propose the three phases' resilience model of the urban sewage treatment system. • Enhance the resilience evaluation in accordance with the failure and recovery processes. • Set the phase and node recovery importance to determine the recovery priority. • Use two situations to illustrate the practicality of the proposed methods. As an important part of resilience city, the urban sewage system has an important impact on the normal operation of the city. However, the majority of recent studies concentrate on a single phase, and multi-phased resilience has not been thoroughly studied. This paper analyzes the multi-phased resilience of the urban sewage treatment system considering the phase performance characteristics. Firstly, the definition of an urban sewage network is given, and the three phases of drainage, treatment, and recycling are analyzed. Secondly, descriptive resilience and mathematical resilience, Residual Resilience, Center of Resilience and Resilience Variance are given to model and assess resilience in accordance with the features of the three phases. What's more, residual resilience model is enhanced in accordance with the failure process and recovery process. Especially for the recovery process, the importance measures are used to set the node recovery importance and phase recovery importance to determine the recovery priority. Finally, a case study in two situations is given to illustrate the practicality and effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

• Analyze the cascading failure for different situations in distribution networks. • Improve the reliability and shorten the cascade failure time by two shunt methods. • Increase network resilience by adding unmanned vehicle delivery tasks. • Propose a time-varying resilience optimization algorithm. • Provide three resilience optimization strategies for distribution networks. With the development of science and technology, unmanned vehicles have become one of the main ways of distribution, and the appearance of unmanned vehicles undoubtedly brings great convenience to people. However, few researchers consider the cascading failure times for different situations in unmanned vehicle distribution networks. Especially, few researchers have integrated them into maintenance strategies to real-time path changes to increase the reliability of accomplishing distribution tasks and improve resilience after congestion. One of the key issues is how to improve the resilience of distribution network and what maintenance strategies should be developed. In this paper, cascading failures are analyzed and resilience is optimized in unmanned vehicle distribution network. First, cascading failures for different situations are analyzed, and two importance-based diversion methods are proposed to describe the three processes of congestion formation, persistence, and evacuation. Second, failure and performance degradation processes are investigated. Third, the Floyd time-varying resilience optimization algorithm is proposed, and the calculation method of resilience under different strategies is given. At last, simulation results show that the proposed strategy 3 improves the original resilience by 101 % compared with the traditional waiting path strategy. [ABSTRACT FROM AUTHOR]

This paper aims to develop a method to construct an asymmetric copula, based on which a closed form of the cumulative bivariate failure rate can be obtained. The construction method differs from existing ones. This new method can facilitate the derivation of some results such as the estimation of the expected number of occurrences for a system whose failure process is modelled by a bivariate stochastic process or the expected cost in optimisation of maintenance policies. [ABSTRACT FROM AUTHOR]

• Analyze the variable system cost in life cycle for critical and non-critical components. • Propose four failure modes to include all possible failure scenarios of the system. • Develop a selection indicator to improve the maintenance strategy for different phases. • Compare with a baseline maintenance by a Huaneng wind farm example. Due to the complexity of multi-component systems, components failure modes are intricate. The failure modes lead to maintenance behavior combinations, which lead to a series of maintenance strategies. However, the failure modes of components are mixed in multi-component systems. Few researchers provide component failure modes comprehensively in life cycle, and integrate them into life cycle maintenance strategies for the selection schemes of different phases. In this paper, a variable system cost methodology in life cycle is studied, and maintenance strategies are developed by identifying components failure modes from a life cycle perspective to improve system reliability. One of the keys is determining maintenance behaviors for components in each phase of life cycle. The proposed four failure modes cover all possible failure scenarios of the components in different phases. Then, a selection scheme is developed to determine maintenance behaviors in life cycle. At last, a case of Huaneng wind farm in China is given to demonstrate the proposed method by comparing with a baseline maintenance strategy. [ABSTRACT FROM AUTHOR]

• Study an importance-based generalized system cost model for different phases in life cycle. • Discuss operation and maintenance costs due to the different types of component failures. • Give a specific selection method for performing end-of-life in case of component failure. • Propose improvement importance to optimize system reliability under invariant resources. • Analyze failure risk under limited and unlimited resource using improvement importance. System life cycle can be divided into four phases: the production phase, the operation phase, maintenance phase and the end-of-life phase. Component failure leads to the different variable costs in different phases. Existing studies have investigated systems from a cost-effectiveness perspective of the operation and maintenance stage, which may not be holistic. Furthermore, the expected failure cost can be used to evaluate the failure risk. In this paper, a generalized system cost for different phases is analyzed in life cycle, then a risk optimization is studied based on an improvement importance. Firstly, a comprehensive life cycle cost model is proposed. Specifically, the operation and maintenance costs due to the different types of component failures are discussed, respectively. Besides, a specific selection method for performing end-of-life in case of component failure is given using the recovery importance. Secondly, an improvement importance is proposed to optimize system reliability under invariant resources. Thirdly, the specific process of the failure risk under limited resource using improvement importance is analyzed. Finally, the proposed methods are verified using two applications, and a discussion on unlimited resources for risk optimization is given. [ABSTRACT FROM AUTHOR]

Effective measurement of system resilience provides a comprehensive understanding of the system's characteristics. However, little research has been devoted to the resilience of a technical system that is affected by both the degradation process of the system and the external shocks. In addition, existing studies have mainly evaluated the resilience of systems without considering competing risks, and rarely investigated the transient resilience evaluation subjected to the interaction of shocks and maintenance. In this paper, a new resilience model is proposed for the systems under competing risks. The paper first introduces a competing risk model to depict the failure modes of the single-component system, and then uses semi-Markov processes to describe the state transition process when the system suffers the attacks of multiple shocks. Then, according to the multi-state division of the system, the resistibility index, absorbability index and recoverability index are proposed and the overall resilience is then introduced. Considering that the system needs to meet the reliability requirement, constrained by limit budget for maintenance, a reliability and cost-based resilience model is proposed. Finally, the case of a radar system subjected to shocks of one type and multiple types of shocks is given to illustrate the concept developed in this paper. [ABSTRACT FROM AUTHOR]

• The total cost of industrial robots is divided into three parts. • Failure mechanism of industrial robot system is analyzed. • An importance measure of preventive maintenance is proposed. • A maintenance strategy is proposed to obtain the priority of components. • The welding robot is used to illuminate the proposed models. The industrial robot plays an increasingly important role in industrial and social activities, and its performance has a great effect on the entire automatic production line. Most studies have analyzed the reliability of industrial robot systems, while the research on preventive maintenance considering multiple costs is limited. This paper proposes two different preventive maintenance strategies for industrial robot systems. Firstly, a preventive maintenance importance measure (PMIM) is proposed by taking into account component maintenance costs, system losses, and component preventive maintenance costs. Subsequently, preventive maintenance strategies are suggested and optimized based on whether the failed component is critical or part of a cut set, in order to determine the priority and optimal number of components for preventive maintenance. Lastly, a welding robot is taken as an example to verify the feasibility of the proposed preventive maintenance strategies. [ABSTRACT FROM AUTHOR]

• According to different failure scenarios, different maintenance strategies are proposed. • A periodic inspection policy and maintenance priority is considered due to external shocks. • Degradation processes of components are modeled with a k-dimensional Wiener process. • An environmental importance of the multi-dimensional degradation process is proposed. Many engineering systems are affected by shocks from their operating environments. When the state of a component degrades to a certain threshold level, preventive maintenance is needed for the purpose of reliability improvement. However, existing studies usually ignore the impact of shocks on different components of a system and therefore on the maintenance policies. This paper proposes to model the degradation processes of components with a k -dimensional Wiener process. Under both deterministic and stochastic environmental conditions, the Eyring model is used to measure the environmental importance of the multi-dimensional degradation process. Based on different failure scenarios, different maintenance strategies are therefore proposed. A periodic inspection policy is considered for each component that may fail due to external shocks. As for multiple components, the maintenance priority is determined based on the joint importance, and optimal preventive maintenance is obtained under the constraint of limited resources. Finally, a robot system is taken as an example to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

• Propose a performance efficiency and cost analysis model for multi-state systems. • Study state and performance rate changes of the system under multiple shocks. • Investigate the cumulative damage effects between shock events. • Investigate the interaction processes of damage and maintenance. • Conduct a case study of a nuclear power plant to demonstrate the proposed model. Real-world systems are often exposed to shocks likes earthquakes and hurricanes during service life, and these shocks may occur multiple times. However, existing studies lack research on damage and maintenance interacting processes under multiple shocks. In this paper, a new performance efficiency and budget surplus rate model for multi-state systems is developed under the interaction of damage and maintenance. System performance efficiency measures the ability of the system to recover its performance from multiple shocks. The budget surplus rate model is introduced for measuring the system's ability to respond to losses from multiple shocks. Multiple cumulative shocks not only cause the system to transfer from a high-performance state to a low-performance state, but also accelerate the performance degradation of the system bringing successive damage, which is reflected by the reduced transition time between states. Markov processes are used to characterize the state transition process between the system suffering damage and maintenance under multiple shock events. A case study of a nuclear power plant is used to demonstrate the proposed methods. Sensitivity analysis of performance efficiency and budget surplus rate is also performed to reflect the shock resistance and maintenance capability of the nuclear power plant system. [ABSTRACT FROM AUTHOR]

• Examine interrelationships among importance measures, maintenance, and resilience. • Analyze importance measure-based resilience on maintenance in the disturbance phase. • Discuss directions of importance measure-based maintenance for resilience. • Summarize maintenance frameworks and specific applications in resilience management. In recent years, frequent natural or man-made disturbances have been accelerating the study of resilience management. As an important source of system resilience, maintenance activities need managing effectively. Meanwhile, reliability importance measures have become an effective tool in maintenance management. However, there are still some challenges in the studies of importance measure-based maintenance management. A comprehensive review and discussion can serve as a useful reference for the future research. This paper firstly reviews the definitions of importance measures, maintenance, and resilience and then examines their interrelationships. It then analyses the roles of importance measures in maintenance management for resilience improvement. Finally, it proposes future research directions. [ABSTRACT FROM AUTHOR]

Highlights • An importance measure is proposed to guide maintenance for repairable systems. • A method based on multi-valued decision diagram is developed to evaluate the measure. • The computational procedure and properties of the proposed measure are illustrated. • A case study is utilized to illustrate the applicability of the measure. Abstract To enhance system performance, corrective maintenance for failed components and preventive maintenance (PM) for operating components can be performed simultaneously on repairable systems. Due to limited budget, it is typically not practical to perform PM for all the operating system components. Moreover, different selections of components for PM can lead to significant differences in system performance improvements. This paper proposes an extended joint integrated importance measure (JIIM) to effectively guide the selection of PM components, aiming to maximize gains of the system performance. A multi-valued decision diagram (MDD) based method is then developed to evaluate the proposed JIIM for general repairable systems. The computational procedure of MDD and some properties of JIIM are illustrated with a numerical example of a system containing three components. A realistic application to the performance analysis of an aircraft warning system verifies the proposed method. [ABSTRACT FROM AUTHOR]

• A new multi-criteria importance measure (MCIM) is proposed in complex engineering systems. • Considering the correlation among criteria, some applications of MCIM are discussed. • The reliability/cost/risk attribute characteristics of MCIM are studied. • The multi-criteria importance is then extended to two common types of complex systems. • The MCIM effectiveness is illustrated by a supply chain system and a train bogie modular system. A wide variety of importance measures have been proposed to rank components for different purposes and most of them are based on a single criterion like reliability, maintenance cost, or risk. In many practical situations, however, people need to evaluate alternatives based on multiple criteria. Thus, the single-criterion importance measure is no longer sufficient for such evaluation. Fewer research has been reported on importance measures applicable to multi-criteria engineering systems, which however fail to consider the correlation among different criteria leading to inaccurate and even misleading importance results. In this paper, a new multi-criteria importance measure (MCIM) is proposed to identify the weakest components in complex engineering systems and it objectively considers the correlation among different criteria. The proposed MCIM is then extended to two common types of complex engineering systems, series hierarchical systems and modular systems. At last, the applications and effectiveness of the proposed MCIM are illustrated by two case studies, including reducing risks of a hierarchical supply chain system and improving the safety of a train bogie modular system. [ABSTRACT FROM AUTHOR]

Importance measures can describe which component reliability change is the most promising if the system structure can be easily changed. Recently, the Birnbaum importance for reconfigurable systems based on the constant reliability has been discussed. This importance shows that importance variation corresponds to the change in system optimal configuration. Traditionally, importance measures do not consider the possible change in a system structure throughout the system's lifetime. However, the possible optimal structural change and the system's lifetime should be considered in importance measures, which can describe the change of component importance with respect to the changes of the component sequencing in optimal system structure during the system lifetime. This paper studies the Birnbaum importance measure, integrated importance measure, and Mean Absolute Deviation with respect to the changes in optimal system structure throughout the system's lifetime. These measures provide useful information regarding the relationships between component reliability and importance measures with the changes in optimal system structure. Finally, examples of linear consecutive- k -out-of- n systems are used to illustrate the utilization of the proposed method. [ABSTRACT FROM AUTHOR]

Preventive maintenance may be performed on a few selected components when a component fails. Importance measures can be used to identify the most important component that requires maintenance. However, this process involves two problems: (a) the preventive maintenance time of the selected component may be bigger than the maintenance time of the failed component; (b) the most important component may incur the highest maintenance cost. Traditional importance measures do not consider the possible effect of maintenance time and cost, which significantly affect the improvement of system reliability. Given the joint effect of component maintenance cost and time on system reliability, this study proposes a cost-based integrated importance measure (IIM) to identify the component or group of components that may be selected for preventive maintenance. The characteristics of cost-based IIM are examined to determine the relationships among failure rates, shape parameters, and the scale parameters of different components. Finally, an application to a wind turbine system is used to illustrate its usage. [ABSTRACT FROM AUTHOR]

Many technical systems are operated under the impact of external factors that may cause the systems to fail. For such systems, an interesting question is how those external factors and their impacts on the system can be identified at an earlier stage. Importance measures in reliability engineering are used to prioritise weak components (or states) of a system. Component failures and the impact of external factors in the real world may be statistically dependent as external factors may affect system performance. This paper proposes a new importance measure for analysing the impact of external factors on system performance. The measure can evaluate the degree of the impact of external factors on the system and can therefore help engineers to identify the factors with the strong impact on the system performance. A real-world case study is used to illustrate its applicability. [ABSTRACT FROM AUTHOR]

With the development of economic globalization and increasing international trade, the maritime transportation system (MTS) is becoming more and more complex. A failure of any supply line in the MTS can seriously affect the operation of the system. Resilience describes the ability of a system to withstand or recover from a disaster and is therefore an important method of disaster management in MTS. This paper analyzes the impact of disasters on MTS, using the data of Suez Canal "Century of Congestion" as an example. In practice, the severity of a disaster is dynamic. This paper categorizes disasters into different levels, which are then modelled by the Markov chain. The concept of a repair line set is proposed and is determined with the aim to minimize the total loss and maximize the resilience increment of the line to the system. The resilience measure of MTS is defined to determine the repair line sequence in the repair line set. Finally, a maritime transportation system network from the Far East to the Mediterranean Sea is used to validate the applicability of the proposed method. [ABSTRACT FROM AUTHOR]

• A maintenance metric for improving the performance of an irrigation network is proposed. • A novel optimum maintenance efficiency model is developed to get the optimal resource allocation. • A pre- and post- disaster management of a complete performance process is systematically analyzed. • An importance measure takes the impact of the deterioration period on yield loss into account. • An irrigation network consisting of 27 nodes is used to verify the practicality of the proposed method. The irrigation network is a critical infrastructure network consisting of reservoirs, canals, and croplands. However, the operation of irrigation networks is often disrupted by natural disasters like droughts, which can lead to serious losses. Timely and effective maintenance can minimize the yield losses. Many maintenance strategies have been proposed to improve the efficiency of maintenance resource utilization and reduce costs. But in the existing literature, the maintenance of irrigation networks under the influence of droughts is still under-explored. To bridge this gap, this paper proposes a maintenance metric for improving the performance of an irrigation network. A novel optimum maintenance efficiency model is then developed to get the optimal resource allocation. A case study, which investigates an irrigation network consisting of 27 nodes, is used to verify the practicality and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

• Cost-informed component maintenance is proposed to guide the optimization of PM policies. • Some theorems are given to illustrate the characters of the proposed index. • A method to optimize the number of components for PM is proposed. • A reactor coolant system is performed to illustrate the applicability of the proposed methods. All systems and components are unreliable in the sense that they will fail. While a failed component in a system is being repaired (i.e., corrective maintenance), preventive maintenance (PM) may be conducted on the other components to improve the reliability of the system. The selection of different components for PM may result in a variety of maintenance policies with different cost implications. It is therefore necessary to develop appropriate tools such as importance measures to guide engineers in selecting components for PM in order to minimize relevant costs. There is little research, nevertheless, that jointly minimizes the total expected cost of maintenance and maximizes the number of components for PM. To fill in this gap, this paper proposes an importance index, Cost-Informed Component Maintenance Index (CICMI). It then derives some propositions of the proposed index and different maintenance policies, respectively. A method to optimize the number of components for PM subject to cost constraints is then proposed. A case study on a reactor coolant system is performed to illustrate the applicability of the proposed methods. [ABSTRACT FROM AUTHOR]

In recent years, the logistic network in combat tends to be complicated with the development of joint operations. When the network is attacked, how to effectively protect it and improve the survivability of the logistic network is vital for the overall performance of the combat system. In this study, the survivability of the logistic network against different attacks is analyzed. Three attack modes are considered, namely random attack, intentional attack, and comprehensive attack with partial information. Network efficiency and effective survival time are defined as the evaluation indexes of the network survivability. Then the importance measure and survivability analysis of the network are carried out. The impact of intentional and random attacks on network survivability in task redistribution mode is calculated. At last, a data simulation is given to demonstrate the proposed method. [ABSTRACT FROM AUTHOR]

• Three different maintenance cost scenarios are analyzed for different maintenance policies. • Considering different cost, components are optimally chosen for preventive maintenance. • The expected costs due to a component and the system are investigated. • Joint loss importance is proposed to determine the expected cost in the system. • A case of the hydraulic system of the aircraft is used to illustrate the proposed method. System safety assessment is a technique aiming at identifying hazards for the system under analysis and showing the compliance with the safety requirements. In order to increase the safety of a system, one may select components in the system for preventive maintenance, under the constraints of maintenance cost, maintenance time and the availability of maintenance staff. In different maintenance policies, maintenance cost can differ. This paper proposes some measures for component preventive maintenance considering maintenance effectiveness, based on which the expected costs due to a component and the system are investigated, respectively. Three different maintenance cost scenarios are analyzed for different maintenance policies. Considering both cost and maintenance constraints, components are optimally chosen for preventive maintenance. An application of a hydraulic system for an aircraft is then used to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

• This paper investigates the capacity of node idle for traffic congestion management. • The paper proposes a traffic transfer principle based on node idle capacity to improve the road maintenance efficiency. • Four types of road networks are analysis in the experiments. • The experimental results show the effectiveness of the proposed traffic transfer principle. Traffic congestion is a universal challenge that affects urban transportation networks, which inevitably age and deteriorate. Maintenance is an essential method for alleviating road congestion. Most of the previous studies concentrate on node load and capacity analysis. The capacity of an idle node is also an important element that affects traffic congestion, such as road damage or traffic accident at the crossroads. To explore the effect of the capacity of an idle node on road congestion, this paper introduces a traffic transfer principle to improve road maintenance efficiency. The nodes of a traffic network can be ranked based on their failure severity. The failure paths of a traffic network can be identified through the internal connections between nodes. Using the transfer time as the weight of each edge and the service time as the weight of each node, this paper proposes a maintenance model to find the shortest repair path for minimizing the maintenance time. To evaluate the proposed model, four different types of road networks are adopted by comparing the maintenance time. The experimental results show the proposed model outperforms previous models. [ABSTRACT FROM AUTHOR]

Importance measures in reliability engineering are used to identify weak components of a system and signify the roles of components in contributing to proper functioning of the system. Recently, an integrated importance measure (IIM) has been proposed to evaluate how the transition of component states affects the system performance based on the probability distributions and transition rates of component states. In the system operation phase, the bathtub curve presents the change of the transition rate of component states with time, which can be described by three different Weibull distributions. The behavior of a system under such distributions can be modeled by the semi-Markov process. So, based on the reported IIM equations of component states, this paper studies how the transition of component states affects system performance under the semi-Markov process. This measure can provide useful information for preventive actions (such as monitoring enhancement, construction improvement, etc.), and provide support to improve system performance. Finally, a simple numerical example is presented to illustrate the utilization of the proposed method. [ABSTRACT FROM AUTHOR]

• Joint importance measures for the optimal structure in multistate systems are extended. • Behaviors of joint importance measures are reflected by the optimal component sequence. • Properties of joint importance with the changes of component reliabilities are analyzed. • Change in joint importance with respect to the optimal system structure is presented. • Differences of generalized measures between the large system and small system are illustrated. For a multi-component system, the impact of the alteration of components on the system reliability often needs assessment. Existing importance measures, however, do not consider the impact of the possible change of the system structure during its life cycle. Therefore, relevant factors should be considered to better reflect the changes in system reliability. To this end, this paper proposes joint importance measures for the optimal component sequence of a consecutive- k -out-of- n system. Incorporating the generalized measures, the paper obtains the joint integrated importance measure and the joint differential importance measure for the optimal component sequence in the binary and multistate consecutive- k -out-of- n systems. Then some properties of the proposed joint importance measures for optimal component sequence are analyzed. Furthermore, this measure reveals the relationship between component reliability and joint importance measure under consideration of consecutive- k- out-of- n system structure changes. Finally, numerical examples are given to demonstrate the applicability of the proposed measures. [ABSTRACT FROM AUTHOR]

The main coolant system (MCS) plays a vital role in the stability and reliability of a nuclear power plant. However, human errors and natural disasters may cause some reactor coolant system components to fail, resulting in severe consequences such as nuclear leakage. Therefore, it is crucial to perform a resilience analysis of the MCS, to effectively reduce and prevent losses. In this paper, a resilience importance measure (RIM) for performance loss is proposed to evaluate the performance of the MCS. Specifically, a loss importance measure (LIM) is first proposed to indicate the component maintenance priority of the MCS under different failure conditions. Based on the LIM, RIMs for single component failure and multiple component failures were developed to measure the recovery efficiency of the system performance. Finally, a case study was conducted to demonstrate the proposed resilience measure for system reliability. Results provide a valuable reference for increasing the system security of the MCS and choosing the appropriate total maintenance cost. [ABSTRACT FROM AUTHOR]

Importance measures in reliability systems are used to identify weak components in contributing to proper functioning of the system. Traditional importance measures mainly concern the change of the system reliability as the change of the reliability of one component and seldom consider the expected number of repairs of the objective component in unit time. This paper proposes an improvement potential rate importance (IPR) to verify the effectiveness of the improvement in system reliability for multi-state repairablek-out-of-n:Gsystems. Then the comparisons between IPR and Birnbaum importance are discussed. Finally, a case study is given to demonstrate the proposed IPR. [ABSTRACT FROM AUTHOR]

Importance measures are widely used to characterize the roles of components in systems. The system lifetime can be divided into different life stages. Traditionally, importance measures do not consider the possible effect of the expected number of component failures over a system's lifetime and over different life stages, which, however, has a great effect on the system performance changes, and should therefore be taken into consideration. This paper extends the integrated importance measure (IIM) from unit time to system lifetime, and to different life stages. Based on the renewal functions of components, this measure can evaluate the changes of the system performance due to component failures. This generalization of the IIM describes which component is the most important to improve the performance of the system during the system lifetime and at different life stages. An example of the application of an oil transportation system is presented to illustrate the use of the generalized IIM. [ABSTRACT FROM PUBLISHER]

• The node and edge failure indicators affecting network stability is proposed. • A failure recovery process for network systems is proposed. • A collaborative approach to the maintenance of nodes and edges in network systems was analyzed. After a major disaster, network systems often face multiple difficulties such as limited time, capital, and resources. Traditional research on recovery after failure often lacks a targeted combination of node maintenance and edge maintenance, which may lead to a situation in which the maintenance cannot be conducted in a timely manner. This paper provides the key factors that affect the stability of the network by the intrinsic associations between nodes and edges in the network, and presents a failure recovery process for network systems. A collaborative approach to the maintenance of nodes and edges in networks is also analyzed. The proposed methods are demonstrated through four different urban transportation networks. Results show that edge failure does not always cause node failure, and node maintenance has a greater impact on network stability than edge maintenance. [ABSTRACT FROM AUTHOR]

• Reliability of UAV swarm based on polygonal consecutive-k-out-of-n systems is proposed. • Reliability of UAV at different locations has different effects on the swarm performance. • Structure optimization of UAV swarm during the mission is studied. • Numerical studies of triangular and quadrilateral UAV swarms are given. The mission reliability of an unmanned aerial vehicle (UAV) swarm is the capability of the swarm to complete its intended missions under specified operating conditions for a specified period of time. In order to achieve high mission reliability, the optimal structure of UAV swarm needs to be determined when some UAVs fail during the mission. In this paper, the mission reliability and structure optimization of UAV swarm are studied based on importance measure. Firstly, the mission reliability model of the UAV swarm based on polygonal linear consecutive- k -out-of- n : F systems is proposed. Secondly, based on the importance measures, the performance of the UAV swarm given different reliability of a UAV at different locations is analyzed. Thirdly, with the three indicators, namely conditional reliability, conditional failure rate, remaining useful life, the structure optimization of UAV swarm during the mission process is analyzed. Numerical examples of triangular and quadrilateral UAV swarms are given to demonstrate the proposed method. The proposed model and metric can be used to support mission planning and the design of a UAV swarm. [ABSTRACT FROM AUTHOR]

Joint reliability importance (JRI) evaluates the interaction of two components in contributing to the system reliability in a system. Traditional JRI measures mainly concern the change of the system reliability caused by the interactive change of the reliabilities of the two components and seldom consider the probability distributions, transition rates of the object component states, and system performance. This article extends the JRI concept of two components from multi-state systems to multi-state transition systems and mainly focuses on the joint integrated importance measure (JIIM) which considers the transition rates of component states. Firstly, the concept and physical meaning of JIIM in binary systems are described. Secondly, the JIIM for deterioration process (JIIMDP) and the JIIM for maintenance process (JIIMMP) in multi-state systems are studied respectively. The corresponding characteristics of JIIMDP and JIIMMP for series and parallel systems are also analyzed. Finally, an application to an offshore electrical power generation system is given to demonstrate the proposed JIIM. [ABSTRACT FROM AUTHOR]

This paper addresses the robust job-shop scheduling problems (RJSSP) with stochastic deteriorating processing times by considering the resilience of the production schedule. To deal with the disturbances caused by the processing time variations, the expected deviation between the realized makespan and the initial makespan is adopted to measure the robustness of a schedule. A surrogate model for robust scheduling is proposed, which can optimize both the schedule performance and robustness of RJSSP. Specifically, the computational burden of simulation is considered a deficiency for robustness evaluation under the disturbance of stochastic processing times. Therefore, a resilience-based surrogate robustness measure (SRM-R) is provided for the robustness estimation in the surrogate model. The proposed SRM-R considers the production resilience and can utilize the available information on stochastic deteriorating processing times and slack times in the schedule structure by analyzing the disturbance propagation of the correlated operations in the schedule. Finally, a multi-objective hybrid estimation of distribution algorithm is employed to obtain the Pareto optimal solutions of RJSSP. The simulation experiment results show that the presented SRM-R is effective and can provide the Pareto solutions with a lower computational burden. Furthermore, an RJSSP case derived from the manufacturing environment demonstrates that the proposed approach can generate satisfactory robust solutions with significantly improved computational efficiency. [ABSTRACT FROM AUTHOR]

This paper mainly focuses on the integrated importance measure (IIM) of component states for maintenance processes. To describe the impact of each component state in maintenance processes, a maintenance cost function of multi-state systems is defined at first. Second, considering the probability distributions, transition rates of the component states, and system maintenance costs, the IIM of component states is described. The corresponding characteristics of the IIM of the component states are discussed in both series systems and parallel systems. Then the relationships between IIM and Griffith importance, Wu importance, mean absolute deviation, and multi-state redundancy importance measures are also discussed. At last, a numerical example is given to demonstrate the IIM of component states. The results show that IIM can be used to identify the most important component state for the maintenance decision. [ABSTRACT FROM AUTHOR]

This paper mainly focuses on the integrated importance measure (IIM) of component states based on loss of system performance. To describe the impact of each component state, we first introduce the performance function of the multi-state system. Then, we present the definition of IIM of component states. We demonstrate its corresponding physical meaning, and then analyze the relationships between IIM and Griffith importance, Wu importance, and Natvig importance. Secondly, we present the evaluation method of IIM for multi-state systems. Thirdly, the characteristics of IIM of component states are discussed. Finally, we demonstrate a numerical example, and an application to an offshore oil and gas production system for IIM to verify the proposed method. The results show that 1) the IIM of component states concerns not only the probability distributions and transition intensities of the states of the object component, but also the change in the system performance under the change of the state distribution of the object component; and 2) IIM can be used to identify the key state of a component that affects the system performance most. [ABSTRACT FROM PUBLISHER]

• It extends the concept of the component maintenance priority (CMP) to other scenarios. • Those scenarios include multistate, continuum, and non-coherent systems, respectively. • It investigates the applications of the proposed measures. If a component in a binary system fails, preventive maintenance (PM) on other components may be conducted while the failed component is being repaired. This raises a question on which components should be selected for PM if maintenance resource is limited. The question can be answered by using the component maintenance priority (CMP) to prioritise components for PM. This paper extends the definition of the CMP to the cases of multi-state systems, continuum systems and non-coherent systems, respectively. It investigates the applications of the proposed measures for multi-state systems in optimisation of maintenance policies and proposes algorithms to minimise maintenance cost. A case study is used to instantiate the validity of the proposed measures. [ABSTRACT FROM AUTHOR]

• The MTS network model based on the main ports and routes is established. • State of the post-disaster MTS is analyzed and the residual resilience is proposed. • Some residual resilience importance methods for the post-disaster MTS are given. • 23 cities' sea routes are used to demonstrate the applicability of the proposed method. In maritime transportation system (MTS), ports and ocean routes are essential for establishing and maintaining effective international trade routes. However, the ability of the ports to send and receive goods can be easily destroyed by political and natural interferences. This will cause a significant negative socio-economic impact such as port operation suspension and route disruption. Effectively implementing resilience management in MTS can therefore improve its ability to handle interruptions and minimizing losses. Based on the post-disaster analysis, this paper proposes a new method to optimize the residual resilience management of ports and routes in MTS and proposes an optimal resilience model. The residual resilience is then applied to some importance measures. The Copeland method is used to comprehensively rank the importance of ports and routes. The restoration priority of interrupted ports and routes of different importance measures for the purpose of minimizing residual resilience is also studied. Sea routes consisting of 23 cities are used to demonstrate the applicability of the proposed method. [ABSTRACT FROM AUTHOR]

• Extended path set space is presented to describe the characteristics of system resilience. • Resilience cube is proposed to measure the system resilience in different states based on the extended path set space. • The resilience measurement can be applied in various phases and adapt to multi-mode/wave shocks scenarios. • A simulation method of resilience cubes is given for system design with random factors. • A maritime unmanned combat system is studied to validate the proposed measurement and method. Resilience is an important property in many engineering systems that may be exposed to shocks. Existing resilience measures primarily focus on changes in system performance during the process of disturbance and recovery. These measures, however, do not directly relate to the composition of a system, which limits the improvement of resilience design. Furthermore, they are also still inadequate in the face of many special situation, such as multi-mode/wave shocks. Therefore, this paper proposes a novel resilience measurement that can be applied to various stage and complex scenarios. First, the concept of the path set is extended to extended path set space (EPSS) to establish the relationship between system design attributes and resilience. Then, resilience cube is defined to measure the system resilience based on EPSS. The measurement represents the properties of the system state itself, including the structure and composition, regardless of the shocks to which the system is exposed. The generality characteristics of the resilience cube are analyzed through different system composition and scenarios. A simulation method of resilience cubes is given for system design with random factors. Finally, the resilience of a maritime unmanned combat system (MUCS) is studied and the superiority of the proposed measurement is proven. [ABSTRACT FROM AUTHOR]

• The cascading failure in a scale-free network is analyzed. • The multi-strategy evolutionary game is used in failure analysis. • The game analysis considers incentive and punishment mechanism. • Useful insights are gained from the analysis of a scale-free network. This research studies the cascading failure in a scale-free network from the perspective of the payoffs of nodes in a multi-strategy evolutionary game. Different from the traditional methods that eliminate nodes randomly or deliberately, this method starts from the payoff of the more general evolutionary game phenomena in reality, and eliminates the nodes with negative payoff and the edges connected with the failed nodes. By eliminating the failure nodes in the scale-free network, we can analyze the influence of the cascade failure on the topological structure of complex networks and discuss the evolutionary direction of the game. Furthermore, the evolutionary game of a ternary strategy considering incentive and punishment mechanism is analyzed, and the influence of the number of law enforcers on the evolutionary game is discussed. We demonstrate the proposed method by conducting a simulation study on a scale-free network. The results show that the aggregation and invulnerability coefficients of the scale-free network are on the rise. Thus, we can conclude that the small group of the network has a positive resistance to the external environment. [ABSTRACT FROM AUTHOR]

• A quantitative indicator based on cost is proposed to measure the supply chain resilience. • Supply chain resilience measurements are analyzed under different customer needs. • Relationships between the resilience indicator and supply chain resilience are discussed. • A numerical example is utilized to illustrate the applicability of the method. In supply chain systems, the entities supplier, manufacturer and distribution center make up the communication platform, which can obtain the data of production, stock, demand, etc. The cyber-physical system (CPS) typically involves multiple computational platforms interacting over communication networks. In the CPS, when the supply chain is disturbed and interruption occurs, supply chain resilience measurement is important to reduce order losses in the supply chain. In this paper, firstly, according to the operational characteristics of different resilience measures, strategy of the supply chain in the interrupted environment is described. Secondly, based on the cost composition of the supply chain operating in the interrupted environment, measurement model of supply chain resilience is established. Thirdly, by introducing the time that the customers can wait as an indicator to represent the external demand environment of supply chain, the customer expectation can be distinguished quantitatively, and the customer expectation factor can be integrated into the measurement model of supply chain resilience. Finally, based on the measurement model of supply chain resilience, quantitative results of the supply chain resilience measurement are obtained, and the relationship between the results and resilience measures is analyzed based on resilience analysis, which illustrates the relationship between the unit capital investment and its ability to reduce order losses. [ABSTRACT FROM AUTHOR]

Importance measures are used to identify weak components and/or states in a system based on the component state random variables, which seem to be inadequate to show the corresponding actual situations. By contrast, the performance random variables own significant practical meanings and eliminate the subjectivity and limitation of state division and definition in many actual situations. In this paper, instead of state random variables, the performance stochastic processes are used for modeling all the components and the entire system, and the integrated importance measure (IIM) for the performance random variables are extended. The generalized IIM evaluates the contribution of component performance to the desired level of system performance. A case study of an oil transmission system is used to illustrate the effectiveness of our approach with importance measures. [ABSTRACT FROM PUBLISHER]

• The reliability of a UAV is analyzed by phased BDD from the perspective of system composition. • The UAV swarm mission is classified several phases and molded by phased n -out-of- k system. • The importance measure is defined to measure the effect of UAV changes on mission reliability. • An optimization model is established to maximize the mission reliability by changing UAV number. • The importance measure and marginal algorithm are combined to solve the optimization model. Nowadays, the missions of the unmanned aerial vehicle (UAV) swarm are very common. However, it is still difficult to calculate the phased mission reliability of UAV swarms. Meanwhile, there is no method to measure the effect of changes in the number of UAVs on reliability. Furthermore, how to determine the number of UAVs in swarm to maximize mission reliability is also a challenging issue. Hence, the reliability of a single UAV is analyzed based on phased binary decision diagram. Then the calculation method of mission reliability is given by modeling the swarm mission as a k -out-of- n system with phased requirements. What's more, some importance measures are proposed to describe the effect of changes in the number of UAVs on mission reliability. In addition, an optimization model is established to maximize mission reliability by reasonably arranging the number of different UAVs in the swarm. The importance measure and marginal optimization algorithm are combined to solve the optimization model. Finally, the change law of mission reliability is analyzed and the advantages of the proposed solving method are demonstrated. [ABSTRACT FROM AUTHOR]

• Practical factor of maintenance cost is comprehensively considered under different maintenance strategies. • New importance measures based on two types of maintenance costs are proposed. • Calculation methods of the proposed measures under the failure-triggered replacement strategy and the age-based replacement strategy are given. • A case study of a propeller plane system is provided to illustrate and validate the proposed method. • Effectiveness of the proposed important measures is investigated in comparison to that of the traditional importance measures As system components and their interactions become more and more complex, system reliability problems become increasingly prominent. In the reliability research, component importance measures have been widely used as an important decision-making aid index. Particularly, importance measures have been used in designing or selecting the optimal maintenance strategy. However, the practical factor of maintenance cost is not comprehensively considered in the existing importance analysis. This paper proposes new importance measures based on two types of maintenance costs under different maintenance strategies, including the failure-triggered replacement strategy that replaces damaged components, the age-based replacement strategy where a component is preventively replaced and when it has been used for a certain period of time, and the hybrid strategy that integrates the former two strategies. Methods for computing the proposed maintenance cost-based importance measures for series systems and parallel systems are given. A case study of a propeller plane system is provided to illustrate and validate the proposed method. [ABSTRACT FROM AUTHOR]

• A resilience evaluation approach for multiplex networks is proposed. • The effectiveness of connectivity link addition for improving the resilience of multiplex networks against attacks is investigated. • A modified connectivity link addition optimization approach is presented to improve the resilience of multiplex networks. Current studies have shifted from the analysis of single-layer network to multi-layer network. However, the performance of multi-layer networks has been significantly influenced by inevitable disturbances; therefore, the resilience of such networks must be maintained. Previous studies on the resilience of multi-layer networks have mainly focused on interdependent networks rather than on multiplex networks, which means that the effectiveness of current methods to improve the resilience of multiplex networks remains limited. To solve these issues, this study develops a two-layer multiplex network and describes failure propagation models by motifs in single-layer and multiplex networks. An approach to evaluate the resilience of multiplex networks is proposed, followed by strategies for its improvement. In particular, an extensive investigation into the effectiveness of connectivity link addition strategies to protect against degree-based targeted attacks is presented. A modified connectivity link addition approach based on degree deviation is proposed to find an optimal strategy under cascading failure to maintain the resilience of multiplex networks from a complex network perspective. Finally, some numerical examples and a real case study of EU-AIR multiplex networks are presented to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract: Binary decision diagram (BDD) is a graph-based representation of Boolean functions. It is a directed acyclic graph (DAG) based on Shannon׳s decomposition. Multi-state multi-valued decision diagram (MMDD) is a natural extension of BDD for the symbolic representation and manipulation of the multi-valued logic functions. This paper proposes a decision diagram extension method based on original BDD/MMDD while the scale of a reliability system is extended. Following a discussion of decomposition and physical meaning of BDD and MMDD, the modeling method of BDD/MMDD based on original BDD/MMDD is introduced. Three case studies are implemented to demonstrate the presented methods. Compared with traditional BDD and MMDD generation methods, the decision diagrams extension method is more computationally efficient as shown through the running time. [Copyright &y& Elsevier]

Abstract: Importance measures are used in reliability engineering to rank the system components according to their contributions to proper functioning of the entire system and to find the most effective ways of reliability enhancement. Traditionally, the importance measures do not consider the possible change of system structure with the improvement of specific component reliability. However, if a component׳s reliability changes, the optimal system structure/configuration may also change and the importance of the corresponding component will depend on the chosen structure. When the most promising component reliability improvement is determined, the component importance should be taken into account with respect to the possible structure changes. This paper studies the component reliability importance indices with respect to the changes of the optimal component sequencing. This importance measure indicates the critical components in providing the system reliability enhancement by both enhancing the component׳s reliability and reconfiguring the system. Examples of linear consecutive-k-out-of-n: F and G systems are considered to demonstrate the change of the component Birnbaum importance with the optimal system reconfiguration. The results show that the change of the importance index corresponds to the change of the system optimal configuration and the importance index can change not monotonically with the variation of the component reliability. [Copyright &y& Elsevier]

Abstract: Importance measures in reliability engineering are used to identify weak components and/or states in contributing to the reliable functioning of a system. Traditionally, importance measures do not consider the possible effect of groups of transition rates among different component states, which, however, has great effect on the component probability distribution and should therefore be taken into consideration. This paper extends the integrated importance measure (IIM) to estimate the effect of a component residing at certain states on the performance of the entire multi-state systems. This generalization of IIM describes in which state it is most worthy to keep the component to provide the desired level of system performance, and which component is the most important to keep in some state and above for improving the performance of the system. An application to an oil transportation system is presented to illustrate the use of the suggested importance measure. [Copyright &y& Elsevier]