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SYSTEM RELIABILITY AND WEIGHTED LATTICE POLYNOMIALS

Published online by Cambridge University Press:  27 May 2008

Alexander Dukhovny  and
Jean-Luc Marichal
Alexander Dukhovny
Affiliation:
Mathematics DepartmentSan Francisco State UniversitySan Francisco, CA 94132 E-mail: dukhovny@math.sfsu.edu
Jean-Luc Marichal
Affiliation:
Mathematics Research UnitUniversity of LuxembourgL-1511 Luxembourg, Luxembourg E-mail: jean-luc.marichal@uni.lu
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Abstract

The lifetime of a system of connected units under some natural assumptions can be represented as a random variable Y defined as a weighted lattice polynomial of random lifetimes of its components. As such, the concept of a random variable Y defined by a weighted lattice polynomial of (lattice-valued) random variables is considered in general and in some special cases. The central object of interest is the cumulative distribution function of Y. In particular, numerous results are obtained for lattice polynomials and weighted lattice polynomials in the case of independent arguments and in general. For the general case, the technique consists in considering the joint probability generating function of “indicator” variables. A connection is studied between Y and order statistics of the set of arguments.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 22 , Issue 3 , July 2008 , pp. 373 - 388
Copyright
Copyright © Cambridge University Press 2008

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