Abstract: The reliability of a discrete time repairable system is studied. There are two components and one repairman in the system. One component is online, the other is cold standby, and the repairman can take multiple vacations. The failure component can be repaired as good as new. The operational time of the unit online, the repair time and the vacation time of the repairman are governed by different discrete phasetype distributions, respectively. The system is studied in a transient and stationary regime. The availability, the conditional probability of failure and the reliability are derived by using the Kronecker operator and the aggregated stochastic process theory. The results show that the discrete case is not a trivial case of the continuous one. Finally, a numerical example is given to illustrate these results.