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Mixture Representations of Residual Lifetimes of Used Systems

Part of: Special processes Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Jorge Navarro ,
N. Balakrishnan  and
Francisco J. Samaniego
Jorge Navarro*
Affiliation:
Universidad de Murcia
N. Balakrishnan*
Affiliation:
McMaster University
Francisco J. Samaniego*
Affiliation:
University of California, Davis
*
∗Postal address: Facultad de Matemáticas, Universidad de Murcia, 30100 Murcia, Spain. Email address: jorgenav@um.es
∗∗Postal address: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada. Email address: bala@mcmaster.ca
∗∗∗Postal address: University of California, Davis, 1 Shields Avenue, Davis, CA 95616, USA. Email address: fjsamaniego@ucdavis.edu
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Abstract

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The representation of the reliability function of the lifetime of a coherent system as a mixture of the reliability function of order statistics associated with the lifetimes of its components is a very useful tool to study the ordering and the limiting behaviour of coherent systems. In this paper, we obtain several representations of the reliability functions of residual lifetimes of used coherent systems under two particular conditions on the status of the components or the system in terms of the reliability functions of residual lifetimes of order statistics.

Keywords

Coherent systemk-out-of-n systemorder statisticssignaturestochastic ordering

MSC classification

Secondary: 60E15: Inequalities; stochastic orderings 60K10: Applications (reliability, demand theory, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 4 , December 2008 , pp. 1097 - 1112
Copyright
Copyright © Applied Probability Trust 2008 

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