Analysis of 2-Unit Standby Redundant Repairable Systems

We discuss three models of 2-unit standby redundant repairable systems subject to one server. These are: I. Warm-standby redundant system with preventive maintenance. The server is always available and is always ready for service. II. Cold-standby redundant system with preventive maintenance. The server is intermittently available. III. Warm-standby redundant system with delay. Delay time is waiting or preparing time for the server. We modify the technique of Markov renewal processes to derive the Laplace-Stieltjes transform of i) distribution of first-passage time to system failure, ii) s-expected number of system failures during (0, t], iii) pointwise unavailability. Several earlier models are shown to be special cases of these models.