Mean residual life estimation

Abdous, Belkacem; Berred, Alexandre

doi:10.1016/j.jspi.2004.06.012

Cited by 26 publications

(10 citation statements)

References 11 publications

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“…It is seen from the table that when the sample size increases the biased and the variance of the estimator tend to decrease. However, as it is mentioned in Abdous and Berred (2005) that (see also Csörgo and Zitikis , 1996) the estimation of the mean residual life for large values of t is a challenging problem in the literature. Unfortunately, as it is seen from Table 1 and Figure 4, the problem holds also for the estimator .…”

Section: Estimation Of R(t)mentioning

confidence: 99%

Evaluation of P(Xt>Yt ) when both Xt and Yt are residual lifetimes of two systems

Zardasht

Asadi

2010

Statistica Neerlandica

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Let the random variables X and Y denote the lifetimes of two systems. In reliability theory to compare between the lifetimes of X and Y there are several approaches. Among the most popular methods of comparing the lifetimes are to compare the survival functions, the failure rates and the mean residual lifetime functions of X and Y. Assume that both systems are operating at time t > 0. Then the residual lifetimes of themrespectively. In this paper, we introduce, by taking into account the age of systems, a time-dependent criterion to compare the residual lifetimes of them. In other words, we concentrate on function R(t ) := P(X t >Y t ) which enables one to obtain, at time t , the probability that the residual lifetime X t is greater than the residual lifetime Y t . It is mentioned, in Brown and Rutemiller (IEEE Transactions on Reliability , 22, 1973) that the probability of type R(t ) is important for designing as long-lived a product as possible. Several properties of R(t ) and its connection with well-known reliability measures are investigated. The estimation of R(t ) based on samples from X and Y is also discussed.

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Section: Estimation Of R(t)mentioning

confidence: 99%

Evaluation of P(Xt>Yt ) when both Xt and Yt are residual lifetimes of two systems

Zardasht

Asadi

2010

Statistica Neerlandica

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“…Downloaded by [Aston University] at 06:18 22 August 2014 Table 2 The total coverage rate, bias, mean-squared error, and relative efficiency of estimators, case (ii) n = m t 0 0 5500 1 0500 2 0000 2 5000 3 0000 4 0000 5.0000 There are several quantitative measures of reliability, e.g., Mean Residual Life (MRL) (c.f. Abdous and Berred, 2005), which are used by practitioners in disciplines such as engineering, medical statistics and finance, to assess the reliability of products and systems. The method discussed in this article could be used to estimate these measures when the underlying distributions are unknown or imprecise.…”

Section: Resultsmentioning

confidence: 99%

On Nonparametric Estimation of a Reliability Function

Zardasht

Zeephongsekul

Asadi

2012

Communications in Statistics - Theory and Methods

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This article considers the properties of a nonparametric estimator developed for a reliability function which is used in many reliability problems. Properties such as asymptotic unbiasedness and consistency are proven for the estimator and using U-statistics, weak convergence of the estimator to a normal distribution is shown. Finally, numerical examples based on an extensive simulation study are presented to illustrate the theory and compare the estimator developed in this article with another based directly on the ratio of two empirical distributions studied in Zardasht and Asadi (2010).

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“…The mean residual life function plays an important role in many fields such as engineering, medicine, life insurance, and demographics. The references from Abdous and Berred (2005), Govil and Aggarwal (1983) provide more details and application. The mean residual life function is defined as…”

Section: Conditional Momentsmentioning

confidence: 99%

Classical and Bayesian methods of estimation for power Lindley distribution with application to waiting time data

Sharma

Singh

2017

CSAM

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The power Lindley distribution with some of its properties is considered in this article. Maximum likelihood, least squares, maximum product spacings, and Bayes estimators are proposed to estimate all the unknown parameters of the power Lindley distribution. Lindley's approximation and Markov chain Monte Carlo techniques are utilized for Bayesian calculations since posterior distribution cannot be reduced to standard distribution. The performances of the proposed estimators are compared based on simulated samples. The waiting times of research articles to be accepted in statistical journals are fitted to the power Lindley distribution with other competing distributions. Chi-square statistic, Kolmogorov-Smirnov statistic, Akaike information criterion and Bayesian information criterion are used to access goodness-of-fit. It was found that the power Lindley distribution gives a better fit for the data than other distributions.

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Mean residual life estimation

Cited by 26 publications

References 11 publications

Evaluation of P(Xt>Yt ) when both Xt and Yt are residual lifetimes of two systems

Evaluation of P(Xt>Yt ) when both Xt and Yt are residual lifetimes of two systems

On Nonparametric Estimation of a Reliability Function

Classical and Bayesian methods of estimation for power Lindley distribution with application to waiting time data

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