On Conditional Inactivity Time of Failed Components in an (n-k+1)-out-of-n System with Nonidentical Independent Components

In this paper, we study an (n-k+1)-out-of-n system by adopting their components to be statistically independent though nonidentically distributed. By assuming that at least m components at a fixed time have failed while the system is still working, we obtain the mixture representation of survival function for a quantity called the conditional inactivity time of failed components in the system. Moreover, this quantity for (n-k+1)-out-of-n system, in one sample with respect to k and m and in two samples, are stochastically compared.