Asymptotic Stability And Reliability Analysis Of A Repairable System With A Deteriorating Standby Unit Under Common-Cause Failure And Critical Human Error

This paper presents a stochastic mathematical model representing two units and one as a standby with critical human error and common cause failure . The deteriorating effect of the standby unit on the system is studied . 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. And by using functional method , the asymptotic stability and reliability analysis of a repairable system is proved , by studying spectral properties of the operator corresponding to this system and by the theory of positive Co- semigroup.