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On the association of the lifelengths of components subjected to a stochastic environment

Published online by Cambridge University Press:  01 July 2016

Claude Lefevre  and
Xavier Milhaud
Claude Lefevre*
Affiliation:
Université Libre de Bruxelles
Xavier Milhaud*
Affiliation:
Université des Sciences et Techniques du Languedoc
*
∗Postal address: Institut de Statistique, CP 210, Université Libre de Bruxelles, Boulevard du Triomphe, B-1050, Bruxelles, Belgique.
∗∗Postal address: Institut de Mathématiques, Université des Sciences et Techniques du Languedoc, Place Eugène Bataillon, F-34060 Montpellier, France.
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Abstract

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This note is concerned with a system of non-renewable components in parallel subjected to a common environment which is described by a real-valued external stochastic process. Given the environment process, the components are supposed to work independently, and the corresponding failure rates are all increasing (or decreasing) functions of the observed current state. It is then proved that, under these assumptions, the association of the external process implies the association of the component lifelengths. Connection with existing results is underlined.

Keywords

FAILURE RATEASSOCIATED VARIABLES
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 22 , Issue 4 , December 1990 , pp. 961 - 964
Copyright
Copyright © Applied Probability Trust 1990 

Footnotes

The paper was written while the author was visiting the Institut de Mathématiques de l'Université des Sciences et Techniques du Languedoc.

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