Analysis of a repairable 2-out-of-3 system with failure and repair times arbitrarily distributed

摘要

A 2-out-of-3 system is a system consists of three components and fails if and only if two components among three fail simultaneously. Each component and system have two states: state of work or state of fail. When a component fails it is put under repair and the two other components stay in functioning with change of their rates of failure. After repair, a component works as new and his actual liftme is the same that the initial. If the failed component is repaired before that the two work component fail; they recovered there initial lifetime. The lifetime and time of repair are independent. In this paper, we propose a technique to calculate the mean duration of repair, the probability of various states of our system and his availability by using the theory of distribution.