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

We study the conditional lifetimes of consecutive k-out-of-n 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.