Abstract: This paper deals with Birolini's duplex system sustained by a non-priority unit in cold standby. It is assumed that the life of the unit is exponential distribution, and the repair time of the unit is general continuous distribution. Then by using supplementary variables approach and generalized Markov process method, the Laplace transform of the reliability and the mean time to first failure are attained. Meanwhile, the availability and the failure frequency of the system are obtained.

Key words: priority rule, Birolini's duplex system, reliability, generalized Markov process