  Here we introduce the idea of using rational expectations, a core concept in
economics and finance, as a tool to predict the optimal failure time for a wide
class of weighted k-out-of-n reliability systems. We illustrate the concept by
applying it to systems which have components with heterogeneous failure times.
Depending on the heterogeneous distributions of component failure, we find
different measures to be optimal for predicting the failure time of the total
system. We give examples of how, as a given system deteriorates over time, one
can issue different optimal predictions of system failure by choosing among a
set of time-dependent measures.
