Reliability Analysis Of Cold Standby Repairable System With Continuous Lifetime Switch

The cold standby repairable system is one of the most important systems in reliability theory and application. This paper presents the reliability analysis of two models as following by using Vector Markov Process theory, Geometric Process theory, linear equation theory, Laplace transform and Laplace-Stieltjes transform.The cold standby system which is composed of two different components and a continuous lifetime switch is studied on the assumption that the repair times of the components are general distributions but the lifetimes of them both have exponential distributions. The switch is not always available. It is supposed that the lifetime and repair time of the switch follow exponential distributions. All random variables are separately independent. And assume that the failed components after repair are "as good as new". By using the theory of Vector Markov Process and tools of Laplace transform and Laplace-Stieltjes transform, some important reliability indexes are derived such as the system's reliability, availability, MTTFF and failure frequency of the system and so on. Moreover, the probability of the repairman's free time is also obtained. Numerical simulation is given when the repair times of the components have exponential and Gamma distributions. We obtain the conclusion that the system is relatively stable. Finally, deducing the system's reliability and MTTFF on the assumption that the switch is perfect to illustrate applications of conclusions obtained above.Geometric process model for a cold standby repairable system with continuous lifetime switch is studied when the two components after repair will not be "as good as new". It is supposed that the repair times of the components have general distributions but the lifetimes of them have exponential distributions. The switch is not always available. The switch can be repaired "as good as new". And assume that the lifetime and repair time of the switch follow exponential distributions. All random variables are separately independent. By using tools of Laplace transform and Laplace-Stieltjes transform, a series of reliability indexes are derived on the basis of the theories of Vector Markov Process and geometric process. Furthermore, the probability of the repairman's free time is also obtained. Finally, the cold standby system of two identical components with perfect switch is discussed when the repair times of components are exponential. Some primary reliability indexes are provided.