Well Posedness and Optimal Check Time of a Repairable System
可修复系统解的渐近稳定性及最优检测时间

The existence of optimal check time of a repairable system with repair time following general distribution is studied. First, the unique existence of the solution of such system is proved. Then, by the positive $C_0$-semigroup generatedby system operator, it is shown that there exists a steady nonnegative solution of the system which is just the normalized eigenvector corresponding toeigenvalue 0 of system operator. At last, based on steady availability of the system, the existence of optimal check time is given.