Stability analysis of a new kind series system

An n-unit series repairable system with a repairman doing other work is discussed in this paper. We are devoted to studying the unique existence of the solution and the exponential stability of the system. C0-semigroup theory is used to prove the existence of a unique non-negative solution of the system. Then by analysing the spectra distribution of the system operator and the quasi-compactness of the system, we derive that the transient solution of the system exponentially converges to the non-negative steady-state solution, which is the eigenvector corresponding to eigenvalue 0 of the system operator. Some reliability indices of the system and the strategy of the repairman doing other work in his idle time are presented at the end of the paper.