Residual lifetimes of ?-out-of-n systems with exchangeable components

Abstract

We consider a (n - ? + 1)-out-of-n system with exchangeable lifetimes of the components. The paper investigates the stochastic ordering properties of the residual lifetime of the system under condition that, at time t, at least (n - r + 1) components are alive. Some results are then extended to the case where the system has a coherent structure with exchangeable components.