Reliability and sensitivity issues are very close and important problems in any technical system. The system’s sensitivity is understood as the dependence of its behavior on changes in some internal parameters. To perform sensitivity analysis, a general procedure based on a theoretical and numerical study is proposed and applied to a repairable k-out-of-n model. The results show the asymptotic insensitivity of the non-stationary and stationary characteristics of the system reliability to the shape of the repair-time distribution, as well as to the value of its coefficient of variation at a fixed mean. The proposed methodology can be useful to researchers and engineers at the designing stage of real systems, as well as applied to other stochastic reliability models.