Further results related to variance past lifetime class &amp; associated orderings and their properties

Mahdy, Mervat

doi:10.1016/j.physa.2016.06.066

Cited by 3 publications

(2 citation statements)

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“…In this case, one wishes to estimate the time that has elapsed since the failure and to study the dispersion of this elapsed interval of time. Therefore, several authors have considered properties and stochastic orders of the variance inactivity time function; see Mahdy [ 38 , 39 ] and Kayid and Izadkhah [ 40 ] and the references therein. Similarly as ( 49 ), one can obtain an analogue representation for the variance inactivity time function in terms of the mean inactivity time function as follows:

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Section: Results On Past Variance and Dgcementioning

confidence: 99%

Generalized Entropies, Variance and Applications

Toomaj

Crescenzo

2020

Entropy

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The generalized cumulative residual entropy is a recently defined dispersion measure. In this paper, we obtain some further results for such a measure, in relation to the generalized cumulative residual entropy and the variance of random lifetimes. We show that it has an intimate connection with the non-homogeneous Poisson process. We also get new expressions, bounds and stochastic comparisons involving such measures. Moreover, the dynamic version of the mentioned notions is studied through the residual lifetimes and suitable aging notions. In this framework we achieve some findings of interest in reliability theory, such as a characterization for the exponential distribution, various results on k-out-of-n systems, and a connection to the excess wealth order. We also obtain similar results for the generalized cumulative entropy, which is a dual measure to the generalized cumulative residual entropy.

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Section: Results On Past Variance and Dgcementioning

confidence: 99%

Generalized Entropies, Variance and Applications

Toomaj

Crescenzo

2020

Entropy

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“…denote the time elapsed after failure until time t, given that the unit has already failed at time t, T ðtÞ having distribution function F ðtÞ ðsÞ ¼ P½tÀT sjT t, and which is known in literature as inactivity time or past lifetime. In recent times, the random variable T ðtÞ has received considerable attention in the literature; see El-Bassiouny and Alwasel (2003), Lai and Xie (2006), Nair and Sudheesh (2010), Mahdy (2012Mahdy ( , 2016, Rezaei, Gholizadeh, and Izadkhah (2015), and Kundu and Sarkar (2017). Consider a probability density function f(t) for a lifetime random variable X with distribution function FðtÞ and survival function FðtÞ ¼ 1ÀF ðtÞ; t 2 R þ : In addition, we assume that the mean life l X ¼ Ð 1…”

Section: T Tmentioning

confidence: 99%

Stochastic Ordering and Reliability Analysis of Inactivity Lifetime with a Cold Standby

Mahdy

2018

American Journal of Mathematical and Management Sciences

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The article discusses truncated inactivity lifetimes for systems with cold standby units. The most common bivariate lifetime distribution was used to clarify these systems. The essay concentrates on the Farlie-Gumbel-Morgenstern family for building a dependence structure between components and to study the properties of suggested systems. The article also compares systems with independent identically distributed components and dependent identically distributed components having the same survival function by using various stochastic orders. Moreover, some applications of the theoretical results of reliability theory are studied.

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