Asymptotic Stability Of The Solution Of A Cold Standby Repairable System

In this paper, we deal with the asymptotic stability of the solution of a cold standby repairable system.In the first chapter, we simply retrospect current status of research of the repairable system home and abroad and introduce the main study content and method.In the second chapter, we introduce the mathematical model corresponding to repairable system which can be described by a group of partial differential equations with integral boundary conditions and fomulated by using supplementary variable technique and probability theory. By Volterra integral theory, we derive the unique existence of solution of the system.In the third chapter, we define the Banach space based on the reality physics background, then define the suitable operator in the Banach space and proves the C₀-semigroup generated by the system oprator is quasi-compact. At the same time, we obtain that all points on the imaginary axis except for zero belong to the resolvent of the system operator. Moreover, we get the asymptotic property of the solution of the sysetem.In the fourth chapter, we discuss the availability, one of the most important indexs of the system reliability , that can be obtained by normalizing the stable solution of the system.