Reliability Analysis Of The System With A Standby Unit And Non-Certainty Switch

On the base of old models, the paper gives three repairable models and the models reliability indexes.Firstly, discusses a two-unit repairable system with a warm standby and priority was studied in this paper. And the switch failure leads to the whole system failure immediately. Using the probability transfer matrix of the system state and the method of Laplace transformation theory, the reliability indexesof this system are obtained under the condition that the lifetime distributions and repair time distributions of the two units are all exponential. We obtain some important reliability indexes of the system. According to this model, we also get some important indexes of some more typical models.Secondly, this paper discusses the system with a cold standby and one maintenance equipment and a repairman. In this system, the maintenance equipment only fails in its working. When it fails, the repairman begins to repair it at once. The maintenance equipment is as good as new after repaired, and it also begins to work immediately when it repaired. The work of the repairman is credible. Suppose the lifetime and the repair time of the unit and the switch are all exponential, the lifetime of the maintenance is exponential, the distribution of repair time of it is general. They are all respectively. This model is studied by using Markov Renew process, so we make the problem simply by using nominal state. When the maintenance equipment is credible, it turns to the typical system with one cold standby unit and the whole system fails when the switch fails. We also get some important reliability indexes.Finally, this paper discusses the two-unit series repairable systems with a cold standby, some units un-repairable, one maintenance equipment and one repairman. Using the supplementary variables method (SVM)and geometry process we get some reliability indexes of this system; besides, using failure time as strategy and expectation benefit which is according to the long running unit time as the goal function, then we obtain the best failure times which make the goal function achieve the maximum value, so the system reliability is guaranteed.