Preservation results for life distributions based on comparisons with asymptotic remaining life under replacements

Bhattacharjee, Manish C.; Abouammoh, A. M.; Ahmed, A. N.; Barry, A. M.

doi:10.1017/s0021900200018180

Cited by 4 publications

(4 citation statements)

References 4 publications

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“…Example 19. Consider the following data in Bhattacharjee et al [9]; these data represent set of 40 patients suffering from It was found that̂= 0.0892 which is greater than the critical value of Table 1. Then we reject the null hypothesis of exponentiality and accept K which states that the data set has NBRU rp property.…”

Section: Numerical Resultsmentioning

confidence: 96%

“…The past decades witnessed some aging notions based on a stochastic comparison between a random life and its equilibrium version * which are introduced and studied (cf. Li and Xu [14], Bhattacharjee et al [9], and Ahmad et al [27]). This section investigates the following new aging notion.…”

Section: Related Aging Classesmentioning

confidence: 97%

“…In literature, it is found that the equilibrium distribution can be used to characterize some aging properties (cf. Bhattacharjee et al [9], Mi [10], Bon and Illayk [11], Mugdadi and Ahmad [12], Bon and Illayk [13], Li and Xu [14], and Kayid et al [15]). The main motivation of our work is a recent paper written by Zardasht and Asadi [2].…”

Section: Introductionmentioning

confidence: 99%

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Residual Probability Function, Associated Orderings, and Related Aging Classes

Kayid

Izadkhah

Alshami

2014

Mathematical Problems in Engineering

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The concept of residual probability plays an important role in reliability and life testing. In this investigation, we study further the residual probability order and its related aging classes. Several characterizations and preservation properties of this order under some statistical and reliability operations of monotone transformation, mixture, weighted distributions, and order statistics are discussed. In addition, by comparing the original distribution with its associated equilibrium distribution with respect to the residual probability order, new aging classes of life distributions are proposed and studied. Finally, a test of exponentiality against such classes is derived and sets of real data are used as examples to elucidate the use of the proposed test for practical problems.

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Section: Numerical Resultsmentioning

confidence: 96%

Section: Related Aging Classesmentioning

confidence: 97%

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Residual Probability Function, Associated Orderings, and Related Aging Classes

Kayid

Izadkhah

Alshami

2014

Mathematical Problems in Engineering

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“…See Bhattacharje, Abouammoh, Ahmed, and Barry [5] and Ahmad and Mugdadi [1] for example. See Bhattacharje, Abouammoh, Ahmed, and Barry [5] and Ahmad and Mugdadi [1] for example.…”

Section: Definition 28: a Lifetime Random Variable X With Finite Meamentioning

confidence: 99%

Some New Reliability Bounds for Sums of Nbue Random Variables

From¹

2010

Prob. Eng. Inf. Sci.

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In this article, we discuss some new upper and lower bounds for the survivor function of the sum of n independent random variables each of which has an NBUE (new better than used in expectation) distribution. In some cases, only the means of the random variables are assumed known. These bounds are compared to the sharp bounds given in Cheng and Lam [6], which requires both means and variances known. Although the new bounds are not sharp, they often produce better upper bounds for the survivor function in the extreme right tail of many NBUE lifetime distributions, an important special case in applications. Moreover, a lower bound exists in one case not handled by the lower bounds of Theorem 3 in Cheng and Lam [6]. Numerical studies are presented along with theoretical discussions.

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Properties of classes of life distribution based on the conditional variance

Stoyanov¹,

Al-Sadi²

2004

J. Appl. Probab.

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We consider two classes of life distribution, V D and V I , the members of which are defined in terms of the conditional variance σ 2(t) of the remaining lifetime of a system: a life distribution F belongs to V D if is a decreasing function and to V I if is increasing. We study closure properties of these classes under relevant reliability operations such as mixing, convolution and formation of coherent systems. We show, for example, that the class V D is not closed under convolution or mixing, and that the class V I is not closed under formation of coherent systems.

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Preservation results for life distributions based on comparisons with asymptotic remaining life under replacements

Cited by 4 publications

References 4 publications

Residual Probability Function, Associated Orderings, and Related Aging Classes

Residual Probability Function, Associated Orderings, and Related Aging Classes

Some New Reliability Bounds for Sums of Nbue Random Variables

Properties of classes of life distribution based on the conditional variance

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