  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.
