Probability in the Engineering & Informational Sciences
Survival analysis (Biometry), Stochastic analysis, Proportional hazards models
In this article, mixture representations of survival functions of residual lifetimes of k-out-of-n systems are obtained when the components are independent but not necessarily identically distributed. Then we stochastically compare the residual lifetimes of k-out-of-n systems in one- and two-sample problems. In particular, the results extend some results in Li and Zhao , Khaledi and Shaked , Sadegh , Gurler and Bairamov  and Navarro, Balakrishnan, and Samaniego . Applications in the proportional hazard rates model are presented as well.
Kochar, S., & Xu, M. (2010). On residual lifetimes of k-out-of-n systems with nonidentical components. Probability in the Engineering & Informational Sciences, 24(1), 109-127.