The Asymptotic Stability Of The Solution Of A Repairable System

A mathematical model of a repairable system with constant human errors,common-cause failure rates and system repair times arbitrarily distributed is discussed.To begin with,the existence and uniqueness of the nonnegative solution of the system is obtained by use of the Volterra operator equation in a Banach space and elementary techniques. Then by the theory of positive C₀- semigroup which is generated by A + E determined by the system,we analysis the spectrum distraction of the system operator. As a result of the stability of semigroup theory of linear operators,we obtain the asymptotic stability of the solution of the repairable system.