On Extreme Residual Lives after the Failure of the System

Abstract

The concept of residual lifetime has attracted considerable research interest in reliability theory. It is useful for evaluating the dynamic behavior of a system. In this paper, we study the extreme residual lives, that is, the minimum and maximum residual lives of the remaining components after the failure of the system. The system is assumed to have an arbitrary structure. We obtain signature-based distributional and ordering results for the extreme residual lives.