Reliability Analysis For The System With Multiple Delay Vacation And System With Repairing Priority

The parallel-series repairable system and the N-unit series repairable system are the two of the most important repairable systems. On the base of the references, the paper has extended some system reliability of repairable models, and gives some system reliability indexes.Firstly, we discussed one parallel-series connection repairable system composed of three-unit. The life of one unit is general continuous distributions, while the life of the others is exponential distribution. And the repair time of the units are all general continuous distributions. Using Probability Theory and the method of Laplace transformation theory, the reliability indexes of this system are obtained: the reliability; the mean time to first failure, the availability, the stead-state failure frequency and so on.Secondly, we discussed the one parallel-series repairable system composed of three units with multiple delay vacation. It is assumed that the life of each unit and the delay vacation time of the repairman are both exponential distribution, and the repair time and the vacation time of the repairman are both general continuous distribution. By using the supplementary variables method and generalized Markov process method, some important reliability indices are obtained: the availability, the mean time to first failure and so on.Finally, we discussed the reliability of an N-unit series repairable system with repairing priority and the repairman doing other work. In this system, the repair time distribution of each unit and the service time for the customer's distribution are assumed to be general continuous distributions, the others to be exponential and the unit of the system to have repairing priority. By using supplementary variable method, the general Markov process method and the tool of the Laplace transform, several reliability indices of this model was obtained and the benefit of the system is discussed.