Abstract: This paper considers a two-dissimilar units cold standby repairable system with a replaceable repair facility and delay repair. By using Markov renewal process theory and total probability decomposition technique, we obtain the reliability indices of system, including the steady state availability, the mean time to the first failure, the steady state failure frequency and the probability of system for repair. Furthermore, by introducing the ``generalized busy period" of the repair facility, we derive both the steady state unavailability and the steady state replaceable frequency of the repair facility. Finally, we present a special case and study the influence of delay repair time and the failure rate of repair facility on several reliability index. In engineering applications, it is very interesting to the steady state reliability quantitative indicators. It is hoped that the results obtained in this paper will provide useful information for optimization design and replacement maintenance of the system.

Key words: cold standby repairable system, delay repair, replaceable repair facility, Markov renewal process, reliability index