This work is dealing with reliability modelling for repairable systems with time dependence. We propose a generalization of reliability indexes such as reliability, interval reliability and availability for homogeneous semi-Markov repairable systems in discrete time. The proposed measure, called sequential interval reliability, is the probability that the system works in a sequence of nonoverlapping time intervals. The necessary framework for calculating that measure according with the asymptotic theory is provided. Finally, numerical results are placed and a brief discussion on the possible applications in real world scenarios is presented. Acknowledgement. The research work of Guglielmo D'Amico was partially supported by the University G. d'Annunzio of Chieti-Pescara, Italy (FAR2020).