Conditional Lifetimes of Consecutive k-Out-of-n Systems

Abstract

We study the conditional lifetimes of consecutive k-out-of-systems. We provide explicit representations for the conditional survival functions of these systems when 2k >= n. The mean residual life functions are obtained, and ordering results are provided. A signature-based evaluation of residual lifetimes is also presented, and some stochastic comparison results are obtained for particular consecutive systems.