Some Results on General Inactivity Time of (n-k+1)-Out-of-n Systems with Dependent Components

The (n-k)-out-of-n systems are important types of coherent systems and have many applications in various areas of engineering. In this paper, the general inactivity time of failed components of (n-k)-out-of-n system is studied when the system fails at time t>0. First we consider a parallel system including two exchangeable components and then using Farlie-Gumbel-Morgenstern copula, investigate the behavior of mean inactivity time of failed components of the system. In the next part, (n-k)-out-of-n systems with exchangeable components are considered and then, some stochastic ordering properties of the general inactivity time of the systems are presented based on one sample or two samples.