System reliability and weighted lattice polynomials

Authors:
Alexander Dukhovny;Jean-luc Marichal
Affiliations:
Mathematics departmentsan francisco state universitysan francisco, ca 94132 e-mail: dukhovny@math.sfsu.edu;Mathematics research unituniversity of luxembourgl-1511 luxembourg, luxembourg e-mail: jean-luc.marichal@uni.lu
Venue:
Probability in the Engineering and Informational Sciences
Year:
2008

Citing 2
Cited 2

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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.