Rational expectations as a tool for predicting failure of weighted k-out-of-n reliability systems

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.