Shock models and testing for the renewal mean remaining life classes

Abouammoh, A. M.; Ahmed, A. N.; Barry, A. M.

doi:10.1016/0026-2714(93)90281-3

Cited by 15 publications

(2 citation statements)

References 13 publications

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“…al. (Abouammoh et al , 1993) introduced a model of accumulated additive damages that cause the failure of a device when it exceeds a certain value threshold. Abouammoh et.…”

Section: Statistical Approach: Moment Inequality Approachmentioning

confidence: 99%

Decreasing renewal dichotomous Markov noise shock model with hypothesis testing applications

Sepehrifar

Yarahmadian

2016

Stat Papers

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In this paper, we investigate the probabilistic characteristics of a unit driven by Dichotomous Markov Noise (DMN), as an external random life increasing and decreasing shocks. Using DMN, we will define two new aging classes of the overall increasing/decreasing (OIL/ODL) nature in the long time behavior, which are separated by an exponential steady state regime. In addition, a moment inequality is derived for the system whose life distribution is in an overall life decreasing (ODL) class. We use this inequality to devise a nonparametric testing procedure for exponentiality against an alternative overall decreasing life distribution.

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“…al. (Abouammoh et al , 1993) introduced a model of accumulated additive damages that cause the failure of a device when it exceeds a certain value threshold. Abouammoh et.…”

Section: Statistical Approach: Moment Inequality Approachmentioning

confidence: 99%

Decreasing renewal dichotomous Markov noise shock model with hypothesis testing applications

Sepehrifar

Yarahmadian

2016

Stat Papers

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“…The dual classes NWRUE and HNWRUE (W ≡ Worse) are similarly defined by reversing the inequalities. The properties (1.2), (1.3) and the corresponding classes of life distributions were introduced by Abouammoh et al (1993), who examined the preservation of these properties under homogeneous Poisson process shock models, and proposed some tests of exponentiality against such alternatives, which have been recently more rigorously explored including testing under censoring schemes (Sen and Bhattacharjee (1998), Bhattacharjee and Sen (1998)). In this paper, we examine the extent to which these classes and their duals satisfy closure properties under standard reliability operations, such as convolutions and mixing, which were not considered previously.…”

Section: Introductionmentioning

confidence: 99%

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

Bhattacharjee

Abouammoh

Ahmed

et al. 2000

Journal of Applied Probability

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We investigate some preservation properties of two nonparametric classes of survival distributions and their duals, under appropriate reliability operations. The aging properties defining these nonparametric classes are based on comparing the mean life of a new unit to the mean residual life function of the asymptotic remaining survival time of the unit under repeated perfect repairs. They are motivated from a point of view that realistic notions of degradation, applicable to repairable systems, should be based on contrasting some aspect of the remaining life of a repairable unit (under a given repair strategy, such as renewals) to the life of a new unit.

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Ageing Concepts

Nair¹,

Sankaran²

2013

Quantile-Based Reliability Analysis

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Shock models and testing for the renewal mean remaining life classes

Cited by 15 publications

References 13 publications

Decreasing renewal dichotomous Markov noise shock model with hypothesis testing applications

Decreasing renewal dichotomous Markov noise shock model with hypothesis testing applications

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

Ageing Concepts

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