Ordering conditional lifetimes of coherent systems

Khaledi, ‎Baha-Eldin; Shaked, Moshe

doi:10.1016/j.jspi.2006.01.012

Cited by 133 publications

(98 citation statements)

References 11 publications

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“…or exchangeable dependent components, especially k-outof-n systems. For instance, see [1], [8], [9], [10], [12], [13], [15], [21], [22], [24], [26], [27], and [28].…”

Section: Mixture Representations Of Inactivity Timesmentioning

confidence: 99%

Mixture Representations of Inactivity Times of Conditional Coherent Systems and their Applications

Zhang

2010

J. Appl. Probab.

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In this paper we obtain several mixture representations of the reliability function of the inactivity time of a coherent system under the condition that the system has failed at time t (> 0) in terms of the reliability functions of inactivity times of order statistics. Some ordering properties of the inactivity times of coherent systems with independent and identically distributed components are obtained, based on the stochastically ordered coefficient vectors between systems.

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“…or exchangeable dependent components, especially k-outof-n systems. For instance, see [1], [8], [9], [10], [12], [13], [15], [21], [22], [24], [26], [27], and [28].…”

Section: Mixture Representations Of Inactivity Timesmentioning

confidence: 99%

Mixture Representations of Inactivity Times of Conditional Coherent Systems and their Applications

Zhang

2010

J. Appl. Probab.

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“…There is a huge reliability literature on the use of stochastic orders which compare locations of the lifetime, residual lifetime or inactivity time of the systems (Khaledi and Shaked (1991)). However, there exist other types of stochastic orders which measure variability and spread.…”

Section: Introductionmentioning

confidence: 99%

Stochastic comparisons of imperfect maintenance models for a gamma deteriorating system

Mercier

Castro

2019

European Journal of Operational Research

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This paper compares two imperfect repair models for a degrading system, with deterioration level modeled by a non homogeneous gamma process. Both models consider instantaneous and periodic repairs. The first model assumes that a repair reduces the degradation of the system accumulated from the last maintenance action. The second model considers a virtual age model and assumes that a repair reduces the age accumulated by the system since the last maintenance action. Stochastic comparison results between the two resulting processes are obtained. Furthermore, a specific case is analyzed, where the two repair models provide identical expected deterioration levels at maintenance times. Finally, two optimal maintenance strategies are explored, considering the two models of repair.

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“…component lifetimes (see Samaniego (1985)) and extended to exchangeable components (see Kochar et al (1999), Navarro et al (2005), Navarro and Eryilmaz (2007), and Navarro et al (2008c)). Further references for various properties of the Samaniego signature, related concepts, and applications are, for instance, Boland et al (2003), Boland and Samaniego (2004b), Navarro and Shaked (2006), Khaledi and Shaked (2007), Navarro and Eryilmaz (2007), Navarro et al (2007aNavarro et al ( ), (2007bNavarro et al ( ), (2008aNavarro et al ( ), (2008b, and Navarro and Hernandez (2008). where X 1 and X 2 are independent random variables that follow a standard exponential distribution with mean 1, and V is a random variable independent of (X 1 , X 2 ) which is distributed according to a gamma distribution with shape parameter a > 0 and scale parameter b > 0.…”

Section: Introductionmentioning

confidence: 99%

Systems with Failure-Dependent Lifetimes of Components

Burkschat¹

2009

J. Appl. Probab.

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A model for describing the lifetimes of coherent systems, where the failures of components may have an impact on the lifetimes of the remaining components, is proposed. The model is motivated by the definition of sequential order statistics (cf. Kamps (1995)). Sequential order statistics describe the successive failure times in a sequential k-out-of-n system, where the distribution of the remaining components' lifetimes is allowed to change after every failure of a component. In the present paper, general component lifetimes which can be influenced by failures are considered. The ordered failure times of these components can be used to extend the concept of sequential order statistics. In particular, a definition of sequential order statistics based on exchangeable components is proposed. By utilizing the system signature (cf. Samaniego (2007)), the distribution of the lifetime of a coherent system with failure-dependent exchangeable component lifetimes is shown to be given by a mixture of the distributions of sequential order statistics. Furthermore, some results on the joint distribution of sequential order statistics based on exchangeable components are given.

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Ordering conditional lifetimes of coherent systems

Cited by 133 publications

References 11 publications

Mixture Representations of Inactivity Times of Conditional Coherent Systems and their Applications

Mixture Representations of Inactivity Times of Conditional Coherent Systems and their Applications

Stochastic comparisons of imperfect maintenance models for a gamma deteriorating system

Systems with Failure-Dependent Lifetimes of Components

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