Abstract
<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We study the conditional lifetimes of consecutive <formula formulatype="inline"> <tex Notation="TeX">$k$</tex></formula>-out-of-<formula formulatype="inline"> <tex Notation="TeX">$n $</tex></formula> systems. We provide explicit representations for the conditional survival functions of these systems when <formula formulatype="inline"> <tex Notation="TeX">$2k\geq n$</tex></formula>. 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. </para>
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