The Study Of Gnedenko System Reliability With Repairman Multiple Vacations

Currently, reliability study is a realy important area of research. Reparable system is one of the most important systems discussed in the reliability theory. The main research of repairable system is the repairman multiple vacations Gnedenko system. Repairman vacation repairable system is only in recent years developed up in the reliability theory. The Gnedenko system is a classic repairable system, so the model is a repairable system model which has practical significance.First roughly summarizes are the development and research of the repairable system, mechanic can leave the system and Gnedenko system in recent years. And the system model of interest is established and the corresponding parameters and conditions are given. And application of functional analysis, it is translated into an abstract Cauchy problem in a Banach space. Secondly, by analyzing the closeness, denseness and dissipative property of the system operator. We obtain a positive compression C0-semigroup of the system operator and the unique existence of the nonnegative time-dependent weak solution of the system is proved by using the strongly continuous semigroup theory. Finally, by analyzing the spectral characteristics of the system operator, we get that0is the system operator simple eigenvalues, the use of semi-group theory of the stability, we obtain the asymptotic stability of solutions of this system.