Analysis of Stability and Reliability of a Class of Repairable Systems

As the development of science and technology,electron productions and network are used everywhere.So the stability analysis of the system becomes more and more important. B.S.Dhillon and N.F.Yang(1993)developed a mathematical model of a(two parrallel identical units working and one on standby)system with human error and arbitrarily distributed repair times by supplementary variable technique.This paper discussed the asymptotic stability and exponential stability of the system solution.We prove that system operators generate a positive C_0-semigroup in the state Banach space.We show that the existence of eigenvalue 0, and 0 is the unique spectral point of the system on the imaginary axis.Further,this paper analyzed the essential spectrum of the system operator before and after perturbation.The results show that the dynamic solution of the systems exponential stability and tends to the steady solution of the system.We can know that the stability of the solution is not necessarily a reliable solution of the system by Maple mapping.This is the practical application of great guiding significance.