Asymptotic Stability And Reliability Analysis Of A Repairable System With Two Non-Identical Unit

This paper presents a stochastic mathematical model representing the parallel repairable system with two non-identical unit. Repair times of the failed system are arbitrarily distributed while all other transition time distributions are negative exponential. 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. Second, studied an eigenvalue corresponding to an eigenvalue and the system is proved nonzero. Last finished the proof of reliability of the system.