Mean residual life functions of finite mixtures, order statistics and coherent systems

Navarro, Jorge; Hernández, Pedro J.

doi:10.1007/s00184-007-0133-8

Cited by 80 publications

(45 citation statements)

References 31 publications

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“…Similar results about the mean residual life of mixture can be found in Mi [13] and Navarro and Hernandez [14].…”

Section: Introductionsupporting

confidence: 85%

Limit of hazard rate function of coherent system with discrete life

2010

Appl Stoch Models Bus & Ind

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In this paper we study the limiting behavior of the hazard rate function of a coherent system S whose components are independent and have discrete lifetimes. The lifetime of the system S can be viewed as the lifetime of a parallel system consisting of the series systems obtained from the minimal paths of S. If we appropriately interpret the 'strongest' minimal path(s) of the system S, it will be shown that the limit of the hazard rate functions of S is the same as that of the 'strongest' path(s) of S. The application of the main results are also provided.

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“…Similar results about the mean residual life of mixture can be found in Mi [13] and Navarro and Hernandez [14].…”

Section: Introductionsupporting

confidence: 85%

Limit of hazard rate function of coherent system with discrete life

2010

Appl Stoch Models Bus & Ind

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“…In recent years several authors have studied the reliability and aging properties of (n − k + 1)-out-of-n systems. Among others, we refer to Asadi (2006), Asadi and Bayramoglu (2006), Bairamov and Arnold (2007), Khaledi and Shaked (2007), Li and Zhang (2008), Li and Zhao (2008), Navarro and Hernandez (2008), , Gurler and Bairamov (2009), Samaniego et al (2009), Navarro and Balakrishnan (2010), Zhang (2010) and Navarro and Shaked (2010). In a recent paper, Kochar and Xu (2010) studied the stochastic properties of the residual lifetime of (n − k + 1)-out-of-n systems under the condition that the components of the system have independent and nonidentical lifetimes.…”

Section: Introductionmentioning

confidence: 99%

Results on the past lifetime of (n − k + 1)-out-of-n structures with nonidentical components

Salehi

Asadi

2010

Metrika

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“…they have the same law as t → ∞); see [7], [8], and [11] for analogous results based on the hazard rate and mean residual life functions.…”

Section: Mixture Representations Of Residual Lifetimes Of Used Systemsmentioning

confidence: 76%

Mixture Representations of Residual Lifetimes of Used Systems

Navarro

Samaniego

2008

J. Appl. Probab.

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The representation of the reliability function of the lifetime of a coherent system as a mixture of the reliability function of order statistics associated with the lifetimes of its components is a very useful tool to study the ordering and the limiting behaviour of coherent systems. In this paper, we obtain several representations of the reliability functions of residual lifetimes of used coherent systems under two particular conditions on the status of the components or the system in terms of the reliability functions of residual lifetimes of order statistics.

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Mean residual life functions of finite mixtures, order statistics and coherent systems

Abstract: Finite mixtures, Mean residual life, Failure rate, Order statistics, Coherent system, k-out-of-n system,

Cited by 80 publications

References 31 publications

Limit of hazard rate function of coherent system with discrete life

Limit of hazard rate function of coherent system with discrete life

Results on the past lifetime of (n − k + 1)-out-of-n structures with nonidentical components

Mixture Representations of Residual Lifetimes of Used Systems

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