Stochastic comparisons of multivariate mixtures

Khaledi, ‎Baha-Eldin; Shaked, Moshe

doi:10.1016/j.jmva.2010.06.018

Cited by 34 publications

(14 citation statements)

References 21 publications

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“…The proof can also be obtained from Equation and Proposition 3.10 in . Now, let us compare systems with the same structure and with DID components having the same copula but different common distributions.…”

Section: The Main Resultsmentioning

confidence: 90%

“…Moreover, it can be used to compare a system with its components (taking h 1 ( u ) = u ). The proofs of (ii) and (iii) can also be obtained from Equation and Propositions 3.6 and 3.8 in , respectively. We must say, here, that when (iv) is used, it might be quite difficult to obtain an explicit expression

h_{1}^{MathClass-bin- 1}

.…”

Section: The Main Resultsmentioning

confidence: 99%

“…Recently, Sordo and Suárez‐Llorens have obtained some new results about stochastic orderings of distorted distributions. Also, some ordering results were obtained in Section 3.2 of Khaledi and Shaked's work .…”

Section: Introductionmentioning

confidence: 99%

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Stochastic ordering properties for systems with dependent identically distributed components

Navarro

Aguila

Sordo

et al. 2012

Appl Stoch Models Bus & Ind

115

106

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In this paper, we obtain ordering properties for coherent systems with possibly dependent identically distributed components. These results are based on a representation of the system reliability function as a distorted function of the common component reliability function. So, the results included in this paper can also be applied to general distorted distributions. The main advantage of these results is that they are distribution-free with respect to the common component distribution. Moreover, they can be applied to systems with component lifetimes having a non-exchangeable joint distribution. Appl. Stochastic ModelsBus. Ind. 2013, 29 264-278 J. NAVARRO ET AL.The rest of the paper is organized as follows. In Section 2, we give the main results of the paper with the general ordering results for distorted distributions and coherent systems with ID components. Specifically, we study properties of the usual stochastic order, hazard rate order, the reversed hazard rate order, the likelihood ratio order, the increasing convex order, the total time on test transform order, and the excess wealth order. In Section 3, we give some examples to show how to apply our general results to specific systems. These examples include systems with IID components and systems with dependent ID components. In Section 4, we give some conclusions and open questions for future research.Throughout the paper, we use the terms increasing and decreasing in a wide sense, that is, a function g is increasing (decreasing) if g.x/ 6 g.y/.>/ for all x 6 y. Whenever we consider an expectation (or a conditional random variable), we assume that it exists. The main resultsLet us consider a coherent system with lifetime T D .X 1 ; : : : ; X n / based on possibly dependent components with lifetimes X 1 ; : : : ; X n , where is the structure function (see [29], Chapter 1). Let us assume that X 1 ; : : : ; X n are identically distributed (ID) with a common reliability function F .t/ D Pr.X i > t/ for i D 1; : : : ; n. The component lifetimes X 1 ; : : : ; X n can be dependent, and this dependence will be represented by the joint reliability (or survival) function of .X

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Section: The Main Resultsmentioning

confidence: 90%

h_{1}^{MathClass-bin- 1}

.…”

Section: The Main Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Stochastic ordering properties for systems with dependent identically distributed components

Navarro

Aguila

Sordo

et al. 2012

Appl Stoch Models Bus & Ind

115

106

View full text Add to dashboard Cite

show abstract

“…Part (a) is proved by Theorem 1.A.6 of Shaked and Shanthikumar (2007) and the assumption that q 1 ðtÞ 6 st q 2 ðtÞ. Similar to part (a), parts (b) and (c) are proved by using Theorem 2.5 of Khaledi and Shaked (2010) and Theorem 1.C.17 of Shaked and Shanthikumar (2007), respectively, and the corresponding assumptions. h Theorem 3.3.…”

Section: Inactivity Times Of Networkmentioning

confidence: 89%

Dynamic network reliability modeling under nonhomogeneous Poisson processes

Zarezadeh

Asadi

2014

European Journal of Operational Research

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“…The proof for lr-ordering is the same by using[20, Theorem 3.5]. (d) This part can be established in the same way as part (c) by using [33, Theorems 1.B.14 and 1.C.17] for hr-and lr-orderings, respectively.…”

mentioning

confidence: 96%

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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Stochastic comparisons of multivariate mixtures

Cited by 34 publications

References 21 publications

Stochastic ordering properties for systems with dependent identically distributed components

Stochastic ordering properties for systems with dependent identically distributed components

Dynamic network reliability modeling under nonhomogeneous Poisson processes

Dynamic Reliability Modeling of Three-State Networks

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