Dynamic network reliability modeling under nonhomogeneous Poisson processes

Zarezadeh, Somayeh; Asadi, Majid

doi:10.1016/j.ejor.2013.07.037

Cited by 19 publications

(6 citation statements)

References 19 publications

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“…Several properties of the reliability function in (7) have been studied by Zarezadeh and Asadi 137 in the case when

N (t)

is a renewal process or is a NHPP. Zarezadeh et al 138 investigated the conditional reliability of the system lifetime under the condition that the components fail under the assumption that the stochastic process

N (t)

is a NHPP.…”

Section: Signature‐based Pm Of Coherent Systems Under Shocksmentioning

confidence: 99%

An overview of some classical models and discussion of the signature‐based models of preventive maintenance

Asadi

Hashemi

2022

Appl Stoch Models Bus & Ind

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In reliability engineering literature, a large number of research papers on optimal preventive maintenance (PM) of technical systems (networks) have appeared based on preliminary many different approaches. According to the existing literature on PM strategies, the authors have considered two scenarios for the component failures of the system. The first scenario assumes that the components of the system fail due to aging, while the second scenario assumes the system fails according to the fatal shocks arriving at the system from external or internal sources. This article reviews different approaches on the optimal strategies proposed in the literature on the optimal maintenance of multi‐component coherent systems. The emphasis of the article is on PM models given in the literature whose optimization criteria (cost function and stationary availability) are developed by using the signature‐based (survival signature‐based) reliability of the system lifetime. The notions of signature and survival signature, defined for systems consisting of one type or multiple types of components, respectively, are powerful tools assessing the reliability and stochastic properties of coherent systems. After giving an overview of the research works on age‐based PM models of one‐unit systems and k‐out‐of‐n systems, we provide a more detailed review of recent results on the signature‐based and survival signature‐based PM models of complex systems. In order to illustrate the theoretical results on different proposed PM models, we examine two real examples of coherent systems both numerically and graphically.

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“…Several properties of the reliability function in (7) have been studied by Zarezadeh and Asadi 137 in the case when

N (t)

N (t)

is a NHPP.…”

Section: Signature‐based Pm Of Coherent Systems Under Shocksmentioning

confidence: 99%

An overview of some classical models and discussion of the signature‐based models of preventive maintenance

Asadi

Hashemi

2022

Appl Stoch Models Bus & Ind

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“…The following lemma from [13] is useful to get some stochastic properties of conditional signature expressed in (6). Before expressing the lemma, we recall that a non-negative function f (x), x ≥ 0, is said to be upside-down bathtub-shaped if it is increasing on [0, a], is constant on [a, b] and is decreasing on [b, ∞) where 0 ≤ a ≤ b ≤ ∞.…”

Section: Residual Lifetime Of a Working Networkmentioning

confidence: 99%

“…In a recent book, Gertsbakh and Shpungin [11] have proposed a new reliability model for a two-state network under the condition that components (with two states) fail according to a renewal process. Motivated by this, Zarezadeh and Asadi [12] and Zarezadeh et al [13] studied the reliability of networks under the assumption that the components are subject to failure according to a counting process. Under the special case that the process of the components' failure is a nonhomogeneous Poisson process (NHPP), they arrived at some mixture representations for the reliability function of the network lifetime and explored its stochastic and aging properties under different conditions.…”

Section: Introductionmentioning

confidence: 99%

Network Reliability Modeling Based on a Geometric Counting Process

2018

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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.

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“…Motivated by this, under the assumption that the failure of the network components occur according to a counting process, Zarezadeh and Asadi [22] investigated various properties of the model in (2) based on different scenarios. Zarezadeh et al [23] studied stochastic properties of dynamic reliability of networks under the assumption that the components fail according to a nonhomogeneous Poisson process (NHPP).…”

Section: Introductionmentioning

confidence: 99%

A Shock Model Based Approachto Network Reliability

2016

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We consider a network consisting of n components (links or nodes) 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 it 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 non-homogeneous Poisson process, explicit form of the network reliability is derived and its aging properties are explored. Several examples are also provided.Networks include a wide variety of real-life systems in communication, industry, software engineering, etc. A network is defined to be a collection of nodes (vertices) and links (edges) in which some particular nodes are called terminals. For instance, nodes can be considered as road intersections, telecommunications switches, servers, and computers; and examples of links can be telecommunication fiber, railways, copper cable, wireless channels, etc.According to the existing literature, a network can be modeled by the triplet N = (V, E, T ), in which V shows the node set, where we assume |V | = m, E stands for link set, with |E| = n, and T ⊆ V is a set of all terminals. When all terminals of the network are connected to each other, the network is called T −connected. We assume that the components (links or nodes) of a network are subject to failure, where the failure of the components may occur according to a stochastic mechanism. A link failure means that the link is obliterated and a node failure means that all links incident to that node are erased. Assuming that the network has two states up, and down, the failure of the components may result in the change of the state of the network.In reliability engineering literature, several approaches are proposed to assess the reliability of a network. An approach, to study the reliability of a network with n components, is based on the assumption that the components of the network have statistically independent and identically distributed (i.i.d.) lifetimes X 1 , X 2 , . . . , X n , and the network has a lifetime T which is a function of X 1 , . . . , X n . An important concept in this approach is the notion of signature that is presented in the following definition; see [17] and [9].Definition 1. Assume that π = (e i 1 , e i 2 , . . . , e in ) is a permutation of the network components numbers. Suppose that all components in this permutation are up. We move along the permutation, from left to right, and turn the state of each component from up to down state. Under the assumption that all permutations are equally likely, the signature vector of the network is defined as s = (s 1 , ..., s n ) wherewh...

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Dynamic network reliability modeling under nonhomogeneous Poisson processes

Cited by 19 publications

References 19 publications

An overview of some classical models and discussion of the signature‐based models of preventive maintenance

An overview of some classical models and discussion of the signature‐based models of preventive maintenance

Network Reliability Modeling Based on a Geometric Counting Process

A Shock Model Based Approachto Network Reliability

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