Tail hazard rate ordering properties of order statistics and coherent systems

Navarro, Jorge

doi:10.1002/nav.20251

Cited by 17 publications

(16 citation statements)

References 22 publications

(17 reference statements)

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“…For example, if α 1 = 2 and α 1 = α 2 = 0.5, then Pr(T 1 ≤ T 2 ) = 0.613, and T 2 is SP-better that T 1 . Comparisons using other criterions can be seen in Shaked and Suarez-Llorens (2003) and Navarro (2007).…”

Section: Applicationsmentioning

confidence: 97%

Comparisons of coherent systems using stochastic precedence

Navarro

Rubio

2010

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The comparisons of coherent systems is a relevant topic in reliability and survival studies. To this purpose, several techniques have been proposed including comparisons of expected lifetimes or comparisons using stochastic orderings. Recently, Samaniego (System Signatures and Their Applications in Engineering Reliability. ) proposed using stochastic precedence to compare the lifetimes of two independent coherent systems. He proved that if the components in both systems are independent and identically distributed (IID), then these comparisons are distribution free, while comparisons based on expected values are not. In the present paper, we obtain new expressions to compare systems using stochastic precedence without the assumption of IID components. In particular, we show that if the components in both systems are independent and satisfy the Cox proportional hazard rate (PHR) model with the same baseline hazard rate, then these comparisons do not depend on the baseline hazard rate function.

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Section: Applicationsmentioning

confidence: 97%

Comparisons of coherent systems using stochastic precedence

Navarro

Rubio

2010

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“…and absolutely continuous, representations of the density and failure rate of the system lifetime are also given in [22]. Some tail-hazard rate ordering properties are given in [14,21].…”

Section: Introductionmentioning

confidence: 99%

On the application and extension of system signatures in engineering reliability

Navarro¹,

Samaniego²,

Balakrishnan³

et al. 2008

Naval Research Logistics

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Following a review of the basic ideas in structural reliability, including signature-based representation and preservation theorems for systems whose components have independent and identically distributed (i.i.d.) lifetimes, extensions that apply to the comparison of coherent systems of different sizes, and stochastic mixtures of them, are obtained. It is then shown that these results may be extended to vectors of exchangeable random lifetimes. In particular, for arbitrary systems of sizes m < n with exchangeable component lifetimes, it is shown that the distribution of an m-component system's lifetime can be written as a mixture of the distributions of k-out-of-n systems. When the system has n components, the vector of coefficients in this mixture representation is precisely the signature of the system defined in Samaniego, IEEE Trans Reliabil R-34 (1985) 69-72. These mixture representations are then used to obtain new stochastic ordering properties for coherent or mixed systems of different sizes.

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“…. ; n. But first, let us recall a well-known and useful result given in [13] which will be used in the sequel.…”

Section: Systems With Components Satisfying Weak Tail Conditionsmentioning

confidence: 99%

“…This type of systems has been studied extensively in the literature (cf. [7][8][9][10][11][12][13][14]). …”

Section: Introductionmentioning

confidence: 99%

Tail behaviour of consecutive 2-within-m-out-of-n systems with nonidentical components

Torrado

2015

Applied Mathematical Modelling

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Consecutive k-within-m-out-of-n systems Hazard rate function Proportional hazard rate model a b s t r a c tWe study the asymptotic behaviour of the hazard rate function of consecutive k-within-mout-of-n systems when k ¼ 2. The consecutive k-within-m-out-of-n systems provide a generalization of consecutive k-out-of-n (m ¼ k) and k-out-of-n (m ¼ n) systems which have been used to model different engineering systems. Here, we consider the case of independent nonidentically distributed component lifetimes. In addition, we obtain some stochastic properties for consecutive 2-within-m-out-of-n systems consisting of components satisfying the proportional hazard rate model.

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Tail hazard rate ordering properties of order statistics and coherent systems

Cited by 17 publications

References 22 publications

Comparisons of coherent systems using stochastic precedence

Comparisons of coherent systems using stochastic precedence

On the application and extension of system signatures in engineering reliability

Tail behaviour of consecutive 2-within-m-out-of-n systems with nonidentical components

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