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

Ashrafi, Somayeh; Asadi, Majid

doi:10.1007/s00184-014-0501-0

Cited by 10 publications

(24 citation statements)

References 30 publications

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“…It is remarkable that the TP 2 property implies associated and associated implies PQD. Consider two systems with respective lifetimes T (1) 1 and T (1) 2 having some shared components, and let S (1) be the corresponding BSM. Assume that the components of the two systems fail according to the SOS X * 1:n , .…”

Section: Definitionmentioning

confidence: 99%

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Reliability modeling of coherent systems with shared components based on sequential order statistics

2018

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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.

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Section: Definitionmentioning

confidence: 99%

“…, F n . Further, assume that T 1 and T 2 are the lifetimes of the systems, respectively, and suppose that I and J are defined as in (1). Proof.…”

Section: Theorem 1 Consider a Pair Of Systems Having Some Shared Commentioning

confidence: 99%

Reliability modeling of coherent systems with shared components based on sequential order statistics

2018

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“…A large number of research works have been published in literature on the reliability and aging properties of multi-state networks and systems under different scenarios. For the recent works on various applications and reliability properties of networks, we refer to [1][2][3][4][5][6][7][8][9][10].…”

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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“…Such a mixture representation has been constructed also for three-state systems with binary components by introducing the concept of two dimensional signatures ( [6], [7], [10]). Recently, Ashrafi & Asadi [1], [2] studied dynamic reliability properties of the three-state systems consisting of binary components. Multi-state systems with multi-state components have a wide range of applications in diverse fields.…”

Section: Introductionmentioning

confidence: 99%

“…Let denote the order statistics corresponding to the th ( , 2) coordinate of . Then the lifetime of the three-state -out-of-:G system can be expressed as (1) and the time that the system enters into state 1 or equivalently the lifetime of the system in state 2 is (2) To make clear the definitions of (1) and (2) , , , , , , , . Then , , , , and , , ,…”

Section: Introductionmentioning

confidence: 99%

Mixture Representations for Three-State Systems With Three-State Components

Eryılmaz

2015

IEEE Trans. Rel.

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This paper is concerned with dynamic reliability modeling of three-state systems consisting of three-state -independent components. The components and the systems are assumed to be in three states: perfect functioning, partial performance, and complete failure. Survival functions of such systems are studied in different state subsets. It is shown that the survival function of a three-state system with a general structure can be represented as a mixture of the survival functions of the three-state -out-of-:G systems. The results are illustrated for the three-state consecutive--out-of-:G systems whose components degrade according to a Markov process.Index Terms-Multi-state systems, order statistics, survival function.

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

Cited by 10 publications

References 30 publications

Reliability modeling of coherent systems with shared components based on sequential order statistics

Reliability modeling of coherent systems with shared components based on sequential order statistics

Network Reliability Modeling Based on a Geometric Counting Process

Mixture Representations for Three-State Systems With Three-State Components

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