In this paper we derive mixture representations for the reliability functions of the conditional residual life and inactivity time of a coherent system with n independent and identically distributed components. Based on these mixture representations we carry out stochastic comparisons on the conditional residual life, and the inactivity time of two coherent systems with independent and identical components.
"On the conditional residual life and inactivity time of coherent systems." J. Appl. Probab. 51 (4) 990 - 998, December 2014.