Reliability Analysis Of Repairable System With Two Types Of Failure And Vacation Of A Repairman

Repairable system with two types of failure is a typical system in reliability theory. Repairman is one of the essential parts of a repairable system, while repairman has vacation or is engaged in other work, which can have the important influence to the system reliability expressions and the economic benefit of the system. Therefore, it has the important theory significance and the application value to consider that repairman has vacation or is engaged in other work in repairable system with two types of failure.This paper studies three repairable system models with two types of failure and multiple vacations of a repairman. These are new ones, which are the spread of the related models in the references and have the important research value.Firstly, a n-unit series repairable system with multiple vacations of a repairman and two types of failure is studied, we obtain the reliability and the mean time to first failure of this system, and using vector Markov process theory and Laplace transform method, we obtain the availability, the failure frequency of this system and the probability of repairman being vacation condition, and so on. In addition, we also discuss the benefit of this system.Secondly, we study a two-unit parallel repairable system with multiple vacations of a repairman and two types of failure. By using vector Markov process theory and Laplace transform method, we obtain the availability, the failure frequency of this system and the probability of repairman being vacation condition, and so on. Then we obtain the Laplace transformation of the reliability and the expressions of the mean time to first failure, and analyze the benefit of this system and determine whether repairman is on vacation strategy.Finally, we discuss a three-unit serie-parallel repairable system with multiple vacations of a repairman and two types of failure. By using vector Markov process theory and Laplace transform method, we obtain the Laplace transformation of the reliability, the expressions of the mean time to first failure, the availability, the failure frequency of this system and the probability of repairman being vacation condition, and so on. Additionally, we also carry on the numerical analysis to the system partial reliability indices and the benefit, and provide the formulation system work plan important basis to the practical work policy-maker.