Hostname: page-component-7bb8b95d7b-5mhkq Total loading time: 0 Render date: 2024-09-13T06:19:50.223Z Has data issue: false hasContentIssue false
  • English
  • Français

On a system of components with joint lifetimes distributed as a mixture of independent exponential laws

Published online by Cambridge University Press:  14 July 2016

Claude Lefèvre  and
Marie-Pierre Malice
Claude Lefèvre*
Affiliation:
Université Libre de Bruxelles
Marie-Pierre Malice*
Affiliation:
University of Kentucky
*
∗Postal address: Université Libre de Bruxelles, Institut de Statistique, C.P. 210, Boulevard du Triomphe, B. 1050 Bruxelles, Belgium.
∗∗Postal address: University of Kentucky, College of Arts and Sciences, Department of Statistics, Lexington, KY 40506-0027, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

A system of n non-renewable components sharing a common environment is considered. The joint lifetimes of the components are taken distributed as a mixture of n independent exponential laws. It is shown how the mixing distribution can affect the number of components functioning and the reliability of a k-out-of-n system. The analysis is carried out by using different partial orderings for distribution functions.

Keywords

RELIABILITY THEORYDEPENDENT FAILURESPARTIAL ORDERINGS FOR DISTRIBUTION FUNCTIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 26 , Issue 1 , March 1989 , pp. 202 - 208
Copyright
Copyright © Applied Probability Trust 1989 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Feller, W. (1968) An Introduction to Probability Theory and its Applications . Wiley, New York.Google Scholar
Lefevre, Cl. and Malice, M.-P. (1988) Comparisons for carrier-borne epidemics in heterogeneous and homogeneous populations. J. Appl. Prob. 25, 663–674.Google Scholar
Lindley, D. V. and Singpurwalla, N. D. (1986) Multivariate distributions for the life lengths of components of a system sharing a common environment. J. Appl. Prob. 23, 418–431.CrossRefGoogle Scholar
Ross, S. M. (1983) Stochastic Processes. Wiley, New York.Google Scholar
Schweder, T. (1981) On the dispersion of mixtures. Scand. J. Statist. 9, 165–169.Google Scholar
Shared, M. (1977) A concept of positive dependence for exchangeable random variables. Ann. Statist. 5, 505–515.Google Scholar
Shared, M. (1980) On mixtures from exponential families. J. R. Statist. Soc. B42, 192–198.Google Scholar
Stoyan, D. (1983) Comparison Methods for Queues and Other Stochastic Models. Wiley, New York.Google Scholar