Coherent systems based on sequential order statistics

Navarro, Jorge; Burkschat, Marco

doi:10.1002/nav.20445

Cited by 42 publications

(31 citation statements)

References 36 publications

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“…, F n (see Navarro and Burkschat (2011)), similar results can be obtained by replacing the PHR assumption with other conditions. Exploiting known results for orderings of sequential order statistics based on F 1 , .…”

Section: Lemma 21 Let P(t) and P(t) Denote The Respective Vectors Osupporting

confidence: 65%

“…The first result of Theorem 2.1 below was obtained in Navarro and Burkschat (2011) and extends a result given in Navarro et al (2008a). The first result of Theorem 2.1 below was obtained in Navarro and Burkschat (2011) and extends a result given in Navarro et al (2008a).…”

Section: Mixture Representations Of Residual Lifetimes and Inactivitysupporting

confidence: 62%

“…Recently, the idea underlying sequential order statistics has been extended to general coherent systems (see Burkschat (2009) and Navarro and Burkschat (2011)). In order to describe component lifetimes in a system, where failures might change the lifetimes of remaining components, a particular dependence model for the components is assumed.…”

Section: Introductionmentioning

confidence: 99%

“…For applications of this representation to orderings of system lifetimes, we refer the reader to Navarro and Burkschat (2011). .…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Signatures of Coherent Systems Based on Sequential Order Statistics

Burkschat¹,

Navarro²

2013

J. Appl. Probab.

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Sequential order statistics can be used to describe the ordered lifetimes of components in a system, where the failure of a component may affect the performance of remaining components. In this paper mixture representations of the residual lifetime and the inactivity time of systems with such failure-dependent components are considered. Stochastic comparisons of differently structured systems are obtained and properties of the weights in the mixture representations are examined. Furthermore, corresponding representations of the residual lifetime and the inactivity time of a system given the additional information about a previous failure time are derived.

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Section: Lemma 21 Let P(t) and P(t) Denote The Respective Vectors Osupporting

confidence: 65%

Section: Mixture Representations Of Residual Lifetimes and Inactivitysupporting

confidence: 62%

Section: Introductionmentioning

confidence: 99%

“…For applications of this representation to orderings of system lifetimes, we refer the reader to Navarro and Burkschat (2011). .…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Signatures of Coherent Systems Based on Sequential Order Statistics

Burkschat¹,

Navarro²

2013

J. Appl. Probab.

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“…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].…”

mentioning

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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Sequential Order Statistics

Cramer

2016

Wiley StatsRef: Statistics Reference Online

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Coherent systems based on sequential order statistics

Cited by 42 publications

References 36 publications

Dynamic Signatures of Coherent Systems Based on Sequential Order Statistics

Dynamic Signatures of Coherent Systems Based on Sequential Order Statistics

Network Reliability Modeling Under Stochastic Process of Component Failures

Sequential Order Statistics

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