Order statistics from mixed exchangeable random variables

Bairamov, Ismihan; Parsi, Safar

doi:10.1016/j.cam.2010.04.030

Cited by 16 publications

(5 citation statements)

References 4 publications

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“…For some results on k-out-of-n systems taking the dependence among the Downloaded by [BYU Brigham Young University] at 16:24 03 January 2015 lifetimes of components into account, see, e.g., Navarro et al (2005Navarro et al ( , 2006, Navarro and Rychlik (2007), and Navarro and Balakrishnan (2010). Bairamov and Parsi (2011) have derived the distribution of a single-order statistic and the joint distribution of two order statistics for a new mixed sample considering two different exchangeable samples.…”

Section: Exchangeability Of the Strengthsmentioning

confidence: 99%

On the Mean Remaining Strength of thek-Out-of-n:FSystem with Exchangeable Components

Bairamov

Gürler

Ucer

2014

Communications in Statistics - Simulation and Computation

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In this article, we consider the mean remaining strength of a k-out-of-n:F system in the stress-strength setup for the exchangeable components. We provide some results for parallel and series systems under this setup, where X 1 , X 2 , . . . , X n are the strengths of the components designed under the common stress. An illustrative example is given for the k-out-of-n:F system using the multivariate FGM distribution.

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Section: Exchangeability Of the Strengthsmentioning

confidence: 99%

On the Mean Remaining Strength of thek-Out-of-n:FSystem with Exchangeable Components

Bairamov

Gürler

Ucer

2014

Communications in Statistics - Simulation and Computation

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“…Let R be the lifetime of an (n − m + 1)-out-of-n : G system subject to random shocks as Marshall-Olkin run shock model. The survival function of the system is When random variables are exchangeable, from [15], S 1 , S 2 , ..., S n…”

Section: Reliability Of An (N − M + 1)-out-of-n : G Systemmentioning

confidence: 99%

On the coherent systems subject to Marshall-Olkin type shocks

Ozkut

Kan

2020

Mathematical Sciences and Applications E-Notes

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Coherent systems and Marshall-Olkin run shock models are combined. Coherent systems consisting of n components receive some kind of shocks from n + 1 different sources similar to Marshall-Olkin type. More precisely, when the component j receive k consecutive fatal shocks from the source j or k consecutive fatal shocks from the source n + 1, it fails, j = 1,. .. ,n. When the interarrival time of shocks has phase-type distribution, reliability, mean time to failure (MTTF) and mean residual life (MRL) function of the coherent systems are studied. Numerical examples and graphical representations are provided.

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“…The standby components which are connected to a system become dependent with system's components due to their placement in the system and system's design. Some studies in this case are found in Navarro et al [15], Bairamov and Parsi [4], Sadegh [20], Eryilmaz and Tank [10], Sadegh [21], Yongjin et al [23]. These studies cover the investigation of lifetime characteristics such as reliability function, mean residual life function, mean time to failure and stochastic ordering results associated with system's lifetime.…”

Section: Introductionmentioning

confidence: 99%

A study on reliability of a $k$-out-of-$n$ system equipped with a cold standby component based on copula

Roy,

Gupta

2021

Preprint

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A k-out-of-n system consisting of n exchangeable components equipped with a single cold standby component is considered. All the components including standby are assumed to be dependent and this dependence is modeled by a copula function. An exact expression for the reliability function of the considered system has been obtained. We also compute three different mean residual life functions of the system. Finally, some numerical examples are provided to illustrate the theoretical results. Our studies subsume some of the initial studies in the literature.

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Order statistics from mixed exchangeable random variables

Cited by 16 publications

References 4 publications

On the Mean Remaining Strength of thek-Out-of-n:FSystem with Exchangeable Components

On the Mean Remaining Strength of thek-Out-of-n:FSystem with Exchangeable Components

On the coherent systems subject to Marshall-Olkin type shocks

A study on reliability of a $k$-out-of-$n$ system equipped with a cold standby component based on copula

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