Comparisons between largest order statistics from multiple-outlier models

Torrado, Nuria

doi:10.1080/02331888.2015.1038268

Cited by 26 publications

(18 citation statements)

References 22 publications

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“…). According to Example 3.4, we take three kinds of Archimedean copulas with ψ 1 (t) = − ln t, ψ 2 (t) = 2(t −0.5 − 1), and ψ 3 (t) = (− ln t) 5 . Figure 2 displays the density functions of X 3:3 and Y 3:3 for these three specified situations, from which one can see that X 3:3 is always more skewed than Y 3:3 , which means that, for a parallel system comprised of three Weibull distributed dependent components, more heterogeneity among these two types leads to larger skewness of the system lifetime distribution.…”

Section: Example 34mentioning

confidence: 99%

“…Pledger and Proschan [32] pioneered comparisons on the order statistics arising from heterogeneous independent exponential variables. After that, many researchers have paid attention to this research direction and its generalization, to name a few, including Balakrishnan and Torrado; Cali, Longobardi, and Navarro; Di Crescenzo; Mesfioui, Kayid, and Izadkhah; Navarro and Spizzichino; Navarro, Torrado, and del Aguila; Proschan and Sethuraman; Zhang and Zhao; Zhang, Amini-Seresht, and Zhao; Zhang et al [5,8,11,26,28,29,33,[37][38][39][40], and a comprehensive review article by Balakrishnan and Zhao [6].…”

Section: Introductionmentioning

confidence: 99%

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On Variability of Series and Parallel Systems With Heterogeneous Components

Zhang¹,

Ding²,

Zhao³

2019

Prob. Eng. Inf. Sci.

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This paper studies the variability of both series and parallel systems comprised of heterogeneous (and dependent) components. Sufficient conditions are established for the star and dispersive orderings between the lifetimes of parallel [series] systems consisting of dependent components having multiple-outlier proportional hazard rates and Archimedean [Archimedean survival] copulas. We also prove that, without any restriction on the scale parameters, the lifetime of a parallel or series system with independent heterogeneous scaled components is larger than that with independent homogeneous scaled components in the sense of the convex transform order. These results generalize some corresponding ones in the literature to the case of dependent scenarios or general settings of components lifetime distributions.

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Section: Example 34mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Variability of Series and Parallel Systems With Heterogeneous Components

Zhang¹,

Ding²,

Zhao³

2019

Prob. Eng. Inf. Sci.

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“…on the respective coordinates (with x (1) i j = · · · = x (r j /2) i j = x i j ). For example, for n = 4 the case (x, x, x, x) for 0 ≤ x ≤ 1 with r 1 = 4 is included in the case (x, x, y, y) for 1 ≥ x ≥ y ≥ 0 with r 1 = 2 and r 2 = 2.…”

Section: Bounds For Systems With Ordered Componentsmentioning

confidence: 99%

“…However, so far, few results have been published for systems with heterogeneous (nonidentically distributed) possibly dependent components. Some comparison results were presented in for parallel systems and in for general coherent systems. Recently, sharp bounds for the system reliability in this general case were derived in .…”

Section: Introductionmentioning

confidence: 99%

Sharp bounds for the reliability of systems and mixtures with ordered components

Miziuła

Navarro

2017

Naval Research Logistics

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In this article, we study how to derive bounds for the reliability and the expected lifetime of a coherent system with heterogeneous ordered components. These bounds can be used to compare the performance of the systems obtained by permuting the components at a given system structure, that is, to study where we should place the different components at a system structure to get the most reliable system. Moreover, a similar procedure is applied to get bounds for mixtures and for the generalized proportional hazard rate model when the baseline populations are ordered. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 108–116, 2017

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“…It should be mentioned that Zhao and Li [20] studied the special case of p = q = 1, and Ding, Da, and Zhao [7] generalized the results in (2) and 3from the multiple-outlier model to the general heterogeneous case.…”

Section: Introductionmentioning

confidence: 99%

Comparisons of Sample Ranges Arising From Multiple-Outlier Models: In Memory of Moshe Shaked

Chen¹,

Zhang²,

Zhao³

2017

Prob. Eng. Inf. Sci.

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In this paper, we discuss the ordering properties of sample ranges arising from multiple-outlier exponential and proportional hazard rate (PHR) models. The purpose of this paper is twofold. First, sufficient conditions on the parameter vectors are provided for the reversed hazard rate order and the usual stochastic order between the sample ranges arising from multiple-outlier exponential models with common sample size. Next, stochastic comparisons are separately carried out for sample ranges arising from multiple-outlier exponential and PHR models with different sample sizes as well as different hazard rates. Some numerical examples are also presented to illustrate the results established here.

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Comparisons between largest order statistics from multiple-outlier models

Abstract: In this work, we discuss stochastic comparisons between the largest order statistics from multiple-outlier models when the numbers of independent and identically distributed random variables are different. That is, if X n:n (p, q) is the largest order statistic among

Cited by 26 publications

References 22 publications

On Variability of Series and Parallel Systems With Heterogeneous Components

On Variability of Series and Parallel Systems With Heterogeneous Components

Sharp bounds for the reliability of systems and mixtures with ordered components

Comparisons of Sample Ranges Arising From Multiple-Outlier Models: In Memory of Moshe Shaked

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