Iranian Statistical Society Journal of the Iranian Statistical Society 1726-4057 19 1 2022 07 23 On Conditional Inactivity Time of Failed Components in an (n-k+1)-out-of-n System with Nonidentical Independent Components 69 83 253792 10.29252/jirss.19.1.69 EN Farkhondeh Alsadat Sajadi Department of Statistics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, Iran. 0000-0001-9692-0941 Mohammad Hossein Poursaeed Department of Statistics, Lorestan University, Khoramabad, Iran. Sareh Goli Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran. Journal Article 2022 07 23 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. https://jirss.irstat.ir/article_253792_883239c6f1ece9dcd8f3d2778f1b8e20.pdf