System reliability and weighted lattice polynomials

Details System reliability and weighted lattice polynomials System reliability and weighted lattice polynomials

2007-12-05

arxiv.org/abs/0712.0707v2

Probability in the Engineering and Informational Sciences 22 (3) (2008) 373-388

Mathematics

Probability

Revised version (minor changes)

Scientific paper

10.1017/S0269964808000223

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 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.

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