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Reliability Engineering and System Safety (18790836)257
An essential goal of reliability engineering is maintaining technical systems optimally, ensuring continuous operation. Random inspections of working systems are crucial in some industries to meet safety and quality standards. This paper proposes an opportunistic optimal age-based preventive maintenance (PM) strategy for n-component (n>1) coherent systems compromising redundant components. The system begins operating at t=0, with a PM time scheduled at TPM. To reduce the risk of unexpected and catastrophic failures, the system is inspected at a random time X before TPM. Based on the information about the number of failed components, m, the operator decides whether to perform the PM action early at X or to allow the system to continue operating on (X,TPM). By incorporating a cost function that considers cost parameters related to failures, we determine the optimal values for the decision variables TPM and m. The paper's results rely on the notion of the system signature as a powerful tool to represent the reliability of n-component systems. To evaluate the effectiveness of the proposed model, we conduct a comprehensive analysis of coherent systems using graphical and numerical examples. In particular, we consider a well-investigated parallel system related to the generator parts in a wind turbine. Using a data set related to the failure times of generators, the applicability of the proposed PM policy is illustrated. © 2025 Elsevier Ltd
In this paper, we consider a (k,ℓ)-out-of-n system with three states: up, partial performance, and down. The system has n binary components and is in up state if at least (n-k+1) out of its components work. The state of partial performance is defined when the number of working components is at least (n-ℓ+1) and less than (n-k+1); k<ℓ. It is assumed that the system is subject to Marshall–Olkin type of shocks where there are n shocks, each of them affects one component and destroys it, and there is one shock that affects all components and destroys simultaneously all of them. Under this scenario, the joint reliability function of state lifetimes and the corresponding singular and absolutely continuous parts are obtained. For the system with the age of t, the mean residual lifetimes of the system states are explored. Some other aging, stochastic, and dependence properties of the system states are investigated, too. We also extend the model for the case where the system is subject to Marshall–Olkin type of shocks in which the arrived shocks may affect one, two,.., or all components and destroy them. Some illustrative examples are also provided to show the applications of the proposed model. © The Author(s) under exclusive licence to Sociedad de Estadística e Investigación Operativa 2025.
Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability (17480078)238(2)pp. 291-303
In this paper, we investigate optimal age-based preventive maintenance (PM) policies for an (n-k + 1)-out-of-n system whose components are exposed to fatal shocks that arrive from various sources. We consider two different scenarios for the system failure. In the first one, it is assumed that the shock process is of the type of Marshall-Olkin where each shock affects one component of the system and puts it down, and one shock affects all components and destroys all of them. In the second scenario, it is assumed that the system is subject to an extended type of Marshall-Olkin shock process where the shocks arriving at random times may cause the breakdown of 1, 2, …, or n components. Under each scenario for the components failure, we investigate an optimal age-based PM model for the system by imposing the related cost function. Then, in each case, we explore the optimal PM time that minimizes the mean cost per unit of time. Some numerical results are presented to illustrate the applications of the proposed models. © IMechE 2023.
Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability (17480078)237(1)pp. 210-227
In this paper, a system consisting of three states: perfect functioning, partial functioning, and down is considered. The system is assumed to be composed of several non-identical groups of binary components. The reliability of the system states under various assumptions on the component lifetimes is investigated. For this purpose, first, a new concept of bivariate survival signature (BSS) is introduced. Then, under the assumption that the component lifetimes of each type are exchangeable dependent, representations for the joint reliability function of the state lifetimes are obtained based on the notion of BSS. In the particular case, three-state systems composed of two types of different modules such as general-series (parallel) systems and systems with component-wise redundancy are investigated. Several examples are presented to illustrate the theoretical results. © IMechE 2022.
Methodology and Computing in Applied Probability (13875841)24(3)pp. 1485-1502
In this paper, we consider two coherent systems having shared components. We assume that in the two systems there are three different types of components; components of type one that just belong to the first system, components of type two that lie only in the second system and components of type three that are shared by the two systems. We use the concept of joint survival signature to assess the joint reliability function of the two systems. Using this concept, some representations for the joint reliability function of the system lifetimes are obtained under two different scenarios of component failures. In the first scenario, we assume that the components of the systems fail according to different counting processes such as non-homogeneous Poisson processes. In the second scenario, it is assumed that the component lifetimes of each type are exchangeable while the three types of component lifetimes can be independent or dependent. To illustrate the theoretical results, two systems with shared components are studied numerically and graphically. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Reliability Engineering and System Safety (18790836)191
In this paper, we consider a network consisting of n components in which the components are subject to shocks arriving based on a counting process. At the occurrence time of each shock, some of components may fail and hence the network fails due to one of these shocks. We propose some preventive maintenance (PM) models based on the notion of t-signature. The proposed PM models are aged-based models relying on the cost and availability criteria. We also extend a time-free PM model which is known as shock-based PM model and explore the number of shocks that minimizes the mean cost per one shock. The advantage of this time-free PM model is that it does not depend on the process of occurrence of the shocks. Some examples are also provided to illustrate the applications of the proposed PM models. © 2019 Elsevier Ltd
IEEE Transactions on Reliability (15581721)67(1)pp. 274-284
This paper is a study on the reliability of a three-state network under shocks in which each shock may cause the failure of more than one component at each time instant. The network is assumed to have n binary components and three states: Up, partial performance, and down. The components are subject to failure due to the occurrence of shocks appearing based on a counting process, and some of the components may fail as a result of each shock. To give a model for the reliability of the network, a new variant of the notion of two-dimensional signature is introduced, which is called two-dimensional t-signature. Based on this new notion, some mixture representations are given for the joint reliability function of the entrance times into a partial performance state T1 and a down state T. Several stochastic orderings and dependence properties regarding T1 and T are provided. The results are also explored for the special case when the shocks appear according to a nonhomogeneous pure birth process under different conditions. © 2018 IEEE.
Mathematics (22277390)6(10)
In this paper, we investigate the reliability and stochastic properties of an n-component network under the assumption that the components of the network fail according to a counting process called a geometric counting process (GCP). The paper has two parts. In the first part, we consider a two-state network (with states up and down) and we assume that its components are subjected to failure based on a GCP. Some mixture representations for the network reliability are obtained in terms of signature of the network and the reliability function of the arrival times of the GCP. Several aging and stochastic properties of the network are investigated. The reliabilities of two different networks subjected to the same or different GCPs are compared based on the stochastic order between their signature vectors. The residual lifetime of the network is also assessed where the components fail based on a GCP. The second part of the paper is concerned with three-state networks. We consider a network made up of n components which starts operating at time t = 0. It is assumed that, at any time t > 0, the network can be in one of three states up, partial performance or down. The components of the network are subjected to failure on the basis of a GCP, which leads to change of network states. Under these scenarios, we obtain several stochastic and dependency characteristics of the network lifetime. Some illustrative examples and plots are also provided throughout the article. © 2018 by the author.
Journal of Applied Probability (00219002)55(3)pp. 845-861
In this paper we are concerned with the reliability properties of two coherent systems having shared components. We assume that the components of the systems are two overlapping subsets of a set of n components with lifetimes X1,...,Xn. Further, we assume that the components of the systems fail according to the model of sequential order statistics (which is equivalent, under some mild conditions, to the failure model corresponding to a nonhomogeneous pure-birth process). The joint reliability function of the system lifetimes is expressed as a mixture of the joint reliability functions of the sequential order statistics, where the mixing probabilities are the bivariate signature matrix associated to the structures of systems. We investigate some stochastic orderings and dependency properties of the system lifetimes. We also study conditions under which the joint reliability function of systems with shared components of order m can be equivalently written as the joint reliability function of systems of order n (n>m). In order to illustrate the results, we provide several examples. Copyright © Applied Probability Trust 2018.
Journal of Applied Probability (00219002)54(4)pp. 1051-1070
In this paper we investigate the stochastic properties of the number of failed components of a three-state network. We consider a network made up of n components which is designed for a specific purpose according to the performance of its components. The network starts operating at time t = 0 and it is assumed that, at any time t > 0, it can be in one of states up, partial performance, or down. We further suppose that the state of the network is inspected at two time instants t 1 and t 2 (t 1 < t 2). Using the notion of the two-dimensional signature, the probability of the number of failed components of the network is calculated, at t 1 and t 2, under several scenarios about the states of the network. Stochastic and ageing properties of the proposed failure probabilities are studied under different conditions. We present some optimal age replacement policies to show applications of the proposed criteria. Several illustrative examples are also provided. Copyright © Applied Probability Trust 2017.
IEEE Transactions on Reliability (15581721)65(2)pp. 992-1000
We consider a network consisting of n components and assume that the network has two states up and down. We further suppose that the network is subject to shocks that appear according to a counting process and that each shock may lead to the component failures. Under some assumptions on the shock occurrences, we present a new variant of the notion of signature which we call t-signature. Then, t-signature-based mixture representations for the reliability function of the network are obtained. Several stochastic properties of the network lifetime are investigated. In particular, under the assumption that the number of failures at each shock follows a binomial distribution and the process of shocks is nonhomogeneous Poisson process, explicit form of the network reliability is derived and its aging properties are explored. Several examples are also provided. © 2015 IEEE.
Journal of Applied Probability (00219002)52(1)pp. 305-305
Metrika (1435926X)78(3)pp. 261-281
Suppose that a system has three states up, partial performance and down. We assume that for a random time T1 the system is in state up, then it moves to state partial performance for time T2 and then the system fails and goes to state down. We also denote the lifetime of the system by T, which is clearly T = T1+T2. In this paper, several stochastic comparisons are made between T, T1 and T2 and their reliability properties are also investigated. We prove, among other results, that different concepts of dependence between the elements of the signatures (which are structural properties of the system) are preserved by the lifetimes of the states of the system (which are aging properties of the system). Various illustrative examples are provided. © 2014, Springer-Verlag Berlin Heidelberg.
Journal of Applied Probability (00219002)51(4)pp. 999-1020
This paper is an investigation into the reliability and stochastic properties of three-state networks. We consider a single-step network consisting of n links and we assume that the links are subject to failure. We assume that the network can be in three states, up (K = 2), partial performance (K = 1), and down (K = 0). Using the concept of the two-dimensional signature, we study the residual lifetimes of the networks under different scenarios on the states and the number of failed links of the network. In the process of doing so, we define variants of the concept of the dynamic signature in a bivariate setting. Then, we obtain signature based mixture representations of the reliability of the residual lifetimes of the network states under the condition that the network is in state K = 2 (or K = 1) and exactly k links in the network have failed. We prove preservation theorems showing that stochastic orderings and dependence between the elements of the dynamic signatures (which relies on the network structure) are preserved by the residual lifetimes of the states of the network (which relies on the network ageing). Various illustrative examples are also provided. © Applied Probability Trust 2014.
Probability in the Engineering and Informational Sciences (02699648)24(4)pp. 561-584
This article develops information optimal models for the joint distribution based on partial information about the survival function or hazard gradient in terms of inequalities. In the class of all distributions that satisfy the partial information, the optimal model is characterized by well-known information criteria. General results relate these information criteria with the upper orthant and the hazard gradient orderings. Applications include information characterizations of the bivariate Farlie-Gumbel-Morgenstern, bivariate Gumbel, and bivariate generalized Gumbel, for which no other information characterization are available. The generalized bivariate Gumbel model is obtained from partial information about the survival function and hazard gradient in terms of marginal hazard rates. Other examples include dynamic information characterizations of the bivariate Lomax and generalized bivariate Gumbel models having marginals that are transformations of exponential such as Pareto, Weibull, and extreme value. Mixtures of bivariate Gumbel and generalized Gumbel are obtained from partial information given in terms of mixtures of the marginal hazard rates. Copyright © 2010 Cambridge University Press.
