Reliability Analysis Of Three-state Standby Repairable System With Delay Repair

Repairable system with three-state is a very typical system in the reliability theory. The series-parallel repairable system, cold standby repairable system and warm standby repairable system are three important repairable systems. On the base of references, the paper has extended the three three-state repairable models and we obtain the reliability indexes of these systems.Firstly, we study geometric process model of a warm standby composed of three-state units with priority. Under the condition of different repairs, it is assumed that one component is given priority but is not as good as new after failure happening, and the standby component is as good as new after failure happening. By using geometric process theory and the method of supplementary variable, we obtain system reliability and the mean time to the first failure of the system.Secondly, we study two typical three-state repairable system of series-parallel and cold standby with delay repair, respectively. In the three-state repairable system of series-parallel, the lifetime distributions of parallel components compared with series component are different exponential distribution, while the delay repair and the repair time distributions of parallel components compared with series component are different generally distribution. The cold standby repairable system consisting of two components, the distribution of lifetime is exponential distribution. the distribution of others components is general continuous distribution. Under the assumption conditions, using the method of supplementary variable and the Laplace transform tools, we obtain Laplace transform formula of some reliability indexes of these two systems such as reliability and availability.Finally, based on these papers, this paper discusses three-state cold standby repairable system with one replaceable facility and delay repair. By using the Markov renewal process theory, the distribution of the time to the first system failure and some primary reliability quantities of the system are obtained.