Stability Analysis of an N-Unit Series Repairable System with a Repairman Doing Other Work

Abstract

We investigate an N-unit series repairable system with a repairman doing other work. By analysing the spectral distribution of the system operator and taking into account the irreducibility of the semigroup generated by the system operator we show that the dynamic solution converges strongly to the steady state solution. Thus we obtain asymptotic stability of the dynamic solution.