Reliability Analysis Of Several Three-State Repairable Systems

Repairable system with three-state is a very typical system in the reliability theory.It has got more and more attention for its universality, scientific and practicality. The paperhas extended several three-state repairable models on the base of references.Firstly, we study a three-state repairable system with a unit, It is assumed that therepairman have multiple delay vacation, the life of the unit and delay vacation time of therepairman are exponential distribution, and the repair time of the unit and the vacationtime of the repairman are general distributions.Secondly, we study a repairable system of three unit-series-parallel connection witha repairman. Under the condition of the series unit has the priority, it is assumed that eachunit have three states, the life of units are exponential distribution, the repair time aftertheir failure happening have general distribution.Then, in the three-state warm standby repairable system with two differentcomponents, assuming the fist unit has priority, and the life of components are exponentialdistribution and the repair time after their failure happening have general distribution.Finally, considering that the influence of switch good or bad to the system, we study3-state cold standby repairable system under the condition of unreliable switch. It isassumed that the switch is not reliable, the life of components and Switch and the repairtime of switch are exponential distribution, and the repair time of units are generaldistribution.Under these assumption conditions, by using the generalized Markov process method,the supplementary variable approach and the Laplace transform tools; we obtain Laplacetransform formula of some reliability indexes of these systems such as reliability andavailability.