Index Life, Ph-type Repair Of Two-component System Reliability Study

Repairable system reliability is an important branch of the reliability theory. Phase type distribution (short for PH distribution) plays a more and more important role in random models researches, being an important tool in queuing theory, inventory theory, reliability research and other random models, completing these problems easily in algorithm. PH distribution makes some random model compute more easily. In random models researches, The PH distribution may be taken over the exponential distribution in the future. The classic two units system have very important role in repairable system. Many specific models can be described in this distribution.On the base of the existing research harvest, the paper has extended some system reliability of the two typical systems.1. This paper considers a cold standby repairable system consisting of two similar units and a single repairman. In the system, the life distributions of these two units are assumed to be the exponential distribution, the repair distribution are assumed to be phase type distribution, and it is "as good as new" after the failed units repair. Under this assumption, by using the Markov process, we obtain some results:(1) The stationary probability distribution, the system reliability and the system availability;(2) The instantaneous probability distributions and the system mean failure time;(3) The distribution of the busy period and the idle period of the repairman.Respectively we prove that the reliability distributions follow PH distribution and busy period distribution of the server and repairman follow PH distribution.2. This paper considers parallel repairable system consisting of two dissimilar units and a single repairman. In the system, the life distributions of these two units are assumed to be the exponential distribution, the repair distribution are assumed to be phase type distribution, and it is "as good as new" after the failed units repair. Under this assumption, by using the Markov process, we obtain some results:(1) The stationary probability distribution, the system reliability and the system availability; (2) The system mean failure time;(3) The distribution of the busy period and the idle period of the repairman.Respectively we prove that the reliability distributions follow PH distribution and busy period distribution of the server and repairman follow PH distribution.