Most of the research on reliability modeling and maintenance optimization focused on a single failure mode, such as soft failure due to system degradation and hard failure due to unexpected shocks. In particular, research attention on multiple dependent competing failure processes (MDCFP) has been growing over the past decade. In comparison to the extant literature devoted to MDCFP, this study is the first research that explores the possible benefits of component reassignment (CR) in extending the system useful lifetime and reducing the maintenance cost subject to the MDCFP. CR was proposed as a resource-efficient maintenance policy for a system of functionally interchangeable components around 2020. In particular, this study makes scientific advancements in reliability modeling of CR-based MDCFP, a mixed binary nonlinear programming model and an efficient matheuristic solution approach for determining the best CR plan and execution time, and a Monte Carlo simulation. Extensive computational results verify that a shuffled-frog-leaping-algorithm (SFLA) based matheuristic method outperforms genetic-algorithm and particle-swarm-optimization based matheuristic methods in terms of solution quality, performance robustness, and computational effort. The SFLA-based matheuristic that combines continuous nonlinear optimization with SFLA is used for the first time to address the CR-related problems. Case studies and sensitivity analysis reveal that the CR tends to be less effective in the environment of heavy and frequent shocks for most systems except the parallel systems. Consequently, ignoring the impact of external shocks would overestimate the effect of CR for most systems and underestimate it for parallel systems. The optimal CR plan and execution time can significantly extend the system useful lifetime in the environment of the MDCFP, especially for systems with low redundancy, and CR is beneficial in reducing maintenance cost if the ratio of the CR cost to the replacement cost is less than the percentage of extending the system useful lifetime.

In industry, many systems exhibit load-sharing characteristics. In a load-sharing system, failure of an asset, in addition to affect system reliability, increases the workloads of remaining surviving assets and so their failure rates. When managing such the assets in a system, it is important for decision makers to ensure overall performance of the system, by determining redundancy of assets and a preventive maintenance plan with consideration of load sharing and uncertain environmental conditions. This article proposes an approach for synthetically optimizing redundancy design and age-based preventive maintenance for a load-sharing system with identical assets. A two-stage stochastic programming model with recourse is established, which incorporates risk-aversion preference of decision makers. A decomposition algorithm is developed to solve the joint optimization model, incorporating analytical properties of system failure rate functions and models. A comparative study with deterministic optimization and robust optimization is conducted to demonstrate the advantages of the proposed risk-averse stochastic programming approach. Finally, a numerical study on an effluent treatment system is conducted to analyze the optimal redundancy design and maintenance plan and practical insights.

Consider a system consisting of multistate components that perform the same function, and each component occupies a location in the system. The deterioration processes of components differ due to different workloads, usage rates, or environmental stresses that are associated with the locations. This article proposes a condition-based maintenance policy, in which the component reallocation (CR) with distinct assignments of components to locations and the preventive replacement of system are dynamically implemented based on the system state. A Markov decision process (MDP) is formulated to optimize the proposed condition-based multi-CR maintenance policy by determining the actions for each system state that minimize the expected long-run system maintenance cost. In the current studies on the MDP for maintenance optimization, the actions mainly include component replacement, imperfect repair, and system replacement. In this article, including CRs of distinct assignments as actions and considering multiple times of CRs increase the action space of the MDP significantly. An enumeration-based value iteration algorithm and a genetic-algorithm-based value iteration algorithm are proposed. Numerical experiments on$k$-out-of-$n$:G systems and Monte Carlo simulation tests show the effectiveness of CRs on reducing the system maintenance cost and extending system lifetime and provide structural insights on the optimal maintenance policy.

This article proposes a new aperiodic preventive maintenance policy, which involves multiple reassignments of components in a system. Considering a multicomponent system, the components deteriorate according to heterogeneous stochastic processes because the components undertake different workloads and environmental stresses. Component reassignment (CR) is an action that reassigns the components to positions during system operation in order to improve overall system performance. The assignments of multiple CRs are mutually dependent decisions, and the execution times to conduct these CRs are also decision variables. All these decisions synthetically impact the system maintenance cost. The reliability functions and failure rates of components under the multiple CRs as well as the side effect of CR action on reducing the component reliability are formulated, using statistical virtual ages that establish links between decisions of consecutive CRs. To optimize the multi-CR based maintenance policy, a binary mixed integer nonlinear programming model is established with the objective of minimizing expected annual system maintenance cost that arises from the CRs, system replacement, and minimal repairs for emergency component failures. The optimal number of CRs is analytically shown to be finite and can be obtained by solving a series of optimization models. This article proposes two matheuristic approaches, an integrative construction approach and a sequential construction approach, to solve the models. Numerical experiments show the application of the proposed model and solution approaches in maintenance policy scheduling.

In a repairable system with multiple functionally interchangeable components, the components may work in different environmental or operational stresses associated with their positions, and thus, experience different failure rates and nonhomogeneous degradation processes. For such a system, the system lifetime can be improved by reassigning the components among the positions in the system after a period of operation. In this sense, the component reallocation (CR) is an option of preventive maintenances. This paper studies a new maintenance policy, which performs periodic preventive system replacements and periodic preventive CRs between system replacements as well as minimal repairs for emergency failures. An optimization model is established to determine the time and assignment for CRs and the time for system replacements with the objective of minimizing expected annual system maintenance cost. The model also justifies if the CR is economically beneficial and deserved to be implemented. The proposed CR-based maintenance policy is further specified for exponential component lifetime distributions and Rayleigh lifetime distributions, and analytical results are derived. Finally, numerical examples for general Weibull lifetime distributions are presented to demonstrate the efficiency and insights of CRs in maintenance.

This paper presents a two-stage stochastic programming model with recourse for integrating the design and sequential preventive maintenance schedule of a system, which is subject to uncertain aperiodic-changing future usage stresses. Specifically, the usage stresses change as the system operates and preventive maintenance is conducted. The system undergoes imperfect repair according to the sequential preventive maintenance policy and minimal repair in response to emergency failures. The system is replaced when the maintenance is uneconomical due to the deterioration of the components. Under such future usage stresses and maintenance, this paper formulates the failure rates and lifetime distributions of components and the system, the failure rates increase with the usage stresses, and both the failure rates and usage stresses have an instantaneous incremental decrease at each preventive maintenance action. In the two-stage stochastic optimization model, the first-stage decision variables are the numbers of components to be used in the subsystems, and these variables affect the second-stage variables, which define the number of imperfect preventive maintenance actions before the replacement of the system and the aperiodic preventive maintenance time intervals for various future usage scenarios. Analytical properties about the failure rates of components and subsystems and the solution for minimizing expected system maintenance cost rate are derived. A decomposition method for solving the proposed two-stage stochastic model is designed based on the analytical results. Numerical examples and sensitivity analysis are provided for deep understanding of the proposed method.

A new modeling approach is presented to optimally and simultaneously design the configuration of a multicomponent system and determine a maintenance plan with uncertain future stress exposure. Traditionally, analytical models for system design and maintenance planning are applied sequentially, but this new model provides an integrated approach to make decisions considering the lifecycle cost of the system. Specifically considering the influence of uncertain future usage stresses on component and system reliability, the integrated redundancy allocation and maintenance planning problem is formulated as a two-stage stochastic programming model with recourse. In this model, the system is exposed to uncertain usage scenarios with their associated probabilities of occurrence or likelihood. The decision variables for the first stage are the selection of component types and the number of components to be used in the system, and these variables are modeled before the uncertainty is revealed. The second-stage variables, involving a recourse function, are the preventive maintenance plan, which defines optimal maintenance times for planned replacement of components under distinct usage scenarios. Numerical examples and sensitivity analysis on series-parallel systems demonstrate applications of the proposed model and provide further insights. The comparisons of the proposed integrated approach to traditional sequential method show advantages of the proposed model in cost saving.

This paper studies a consecutive- k-within- m-out- of- n:F system with Markov-dependent components; that is, the reliability of a component depends on its neighbors. Using probability generating functions, the closed-form formula for reliability of the consecutive- k-within- m-out-of- n:F system with Markov-dependent components and a closed-form formula for joint reliability importance (JRI) of two components in such a system are derived. The JRI of two components evaluates the interaction effect between the components on contributing to system reliability. A formula of the JRI of more than two components are also derived and presented. Many real systems and procedures, such as radar detection systems, pipeline systems, quality inspection procedures, and so on, can be modeled as a consecutive- k-within- m-out-of- n:F system, in which components are Markov-dependent. The present results can evaluate the reliability of these systems or the accuracy of the procedures as well as the contributions of components to the system reliability or the accuracy of the procedures. The applications of the present formulas are demonstrated through the numerical examples. The examples show the changes of system radiabilities and the changes among the JRI values of different pairs of components in consecutive- k-within- m-out-of- n:F systems. The JRI values of Markov-dependent components are also compared to the JRI values of s-independent components.

The Joint Reliability Importance (JRI) of two components evaluates the interaction effect between the components on system reliability. This paper focuses on the JRI of components in a consecutive- k-out-of- n:F system, and an m-consecutive- k- out-of- n:F system, both with Markov-dependent components. We derive the closed-form formulas of the JRI of two components using probability generating functions, and extend the results to the JRI of three and more components. We further provide exact conditional distributions of random variables which are used in probability generating functions for determining the JRI of two components. Our numerical examples and tests demonstrate the use of derived formulas, and provide further insights about the JRI for Markov-dependent components.

Many importance measures have been proposed with respect to the diverse considerations of system performance, reflecting different probabilistic interpretations and potential applications. This paper studies importance measures in reliability, including their definitions, probabilistic interpretations, properties, computations, and comparability. It categorizes importance measures into the structure, reliability, and lifetime types based on the knowledge for determining them. It covers importance measures of individual components, and ones of pairs and groups of components. It also investigates importance measures in consecutive-k-out-of-nsystems.

To identify the critical components or sets of components in a system, various importance measures have been proposed with different probabilistic perspectives and applications. Many of these importance measures are actually related to each other in some ways. This paper summarizes the importance measures in reliability, and presents relations and comparisons among them, focusing on their interrelations to the B-importance, the dominant relations among them, the dual relations, their performances in typical systems, and their computations. The early versions of the importance measures are for binary coherent systems, while the recent research is not limited to this type of system. This paper investigates the extensions of importance measures in noncoherent systems, multistate systems, continuum systems, and repairable systems.

The paper by Hwang (IEEETrans.Reliability, vol. 54, no.1, p. 169-172, 2005) presented structural importance measures in terms of cutsets or pathsets, and investigated how they are related. Hwang's paper has made contributions to importance measures. However, several errors which cause confusions are found in the paper. This note is to clarify these errors, and discuss the suspicions.