Computing and Applying the Signature of a System With Two Common Failure Criteria

Eryılmaz, Serkan; Zuo, Ming J.

doi:10.1109/tr.2010.2054170

Cited by 39 publications

(30 citation statements)

References 25 publications

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“…For signature based properties of coherent systems, we refer the reader, among others, to Asadi and Goliforushani (2008), Eryilmaz and Zuo (2010), Eryilmaz (2011b), Kelkin Nama et al (2013, Khaledi and Shaked (2007), Navarro et al (2008aNavarro et al ( , 2010Navarro et al ( , 2008b, Samaniego (1985Samaniego ( , 2007 and Zhang (2010a,b).…”

mentioning

confidence: 99%

On the stochastic and dependence properties of the three-state systems

Ashrafi

Asadi

2014

Metrika

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Suppose that a system has three states up, partial performance and down. We assume that for a random time T 1 the system is in state up, then it moves to state partial performance for time T 2 and then the system fails and goes to state down. We also denote the lifetime of the system by T , which is clearly T = T 1 + T 2 . In this paper, several stochastic comparisons are made between T , T 1 and T 2 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.

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confidence: 99%

On the stochastic and dependence properties of the three-state systems

Ashrafi

Asadi

2014

Metrika

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“…The network fails when exactly two (three) nodes fail in 8 (16) situations out of 24. After the failure of three nodes, the network is always down.…”

Section: Network Reliability Under a Counting Process Of Componenmentioning

confidence: 99%

“…Many D-spectrum based properties of reliability (1) have been studied in recent years by several authors. Among the large number of research works that have appeared in literature, one can refer to [4], [12]- [16], [19], [31], [32], [37], [41], and [47].…”

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confidence: 99%

Network Reliability Modeling Under Stochastic Process of Component Failures

Zarezadeh

Asadi

2013

IEEE Trans. Rel.

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The concept of D-spectrum is a useful tool to investigate the reliability and stochastic properties of networks. In this paper, we consider a network consisting of components (links or nodes), and assume that the network has two states: up, and down. We study the D-spectrum-based reliability of the network under the assumption that the components are subject to failure according to a counting process. Mixture representation of the reliability of the network lifetime is given in terms of the reliability functions of arrival times. It is shown that, when the D-spectra of two networks are stochastically ordered, then under some conditions the lifetimes of two networks are also stochastically ordered. Under the special case when the process of the failure of the components is a nonhomogeneous Poisson process, we arrive at a mixture representation for the reliability function of the network lifetime, and explore several stochastic and aging properties of the network lifetime under different scenarios. The failure rate of the network lifetime and its asymptotic behavior is investigated. D-spectrum based representation theorems are also given on the basis of the stochastic precedence concept.Index Terms-D-spectrum, increasing failure rate, nonhomogeneous Poisson process, record values, stochastic ordering, stochastic precedence, system signature, two-state networks. ACRONYMSAND ABBREVIATIONS NHPP Nonhomogeneous Poisson process NBU New better than used NWU New worse than used MRL Mean residual lifetime m.v.f. Mean value function IFR Increasing failure rate DFR Decreasing failure rate NOTATIONS the node set of network the link set of network Manuscript

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“…The concept of the signature is found to be a useful tool in the study of reliability and ageing properties of networks and coherent systems having two states. For recent developments on the reliability of the networks and coherent systems based on the notion of the signature, we refer the reader to, among others, [3], [5], [7]- [9], [11], [12], [15], [16], [18], [25]- [29], and [35]- [37].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Reliability Modeling of Three-State Networks

Ashrafi¹,

Asadi²

2014

J. Appl. Probab.

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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.

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Computing and Applying the Signature of a System With Two Common Failure Criteria

Cited by 39 publications

References 25 publications

On the stochastic and dependence properties of the three-state systems

On the stochastic and dependence properties of the three-state systems

Network Reliability Modeling Under Stochastic Process of Component Failures

Dynamic Reliability Modeling of Three-State Networks

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