中文摘要：

研究了一类修理工可多重延误休假且带预警装置的简单可修复系统，其中系统的失效率和修理工的延误休假率均与系统的运行时间有关．首先运用概率分析的方法将系统模型表示为一组积-微分方程，然后将系统方程转化为一个Banach空间中的抽象半线性发展方程的初值问题，并利用G0半群理论讨论了系统解的存在惟一性条件．

英文摘要：

In this paper, a new kind of simple repairable system with repairman vacation and warning device is discussed, in which the failure rate functions of the unit and the de- layed vacation rate function of the repairman are related to the working time of the system. The system model of a group of integro-differential equations is established by using prob- ability analysis method, which then is translated into a initial value problem of a class of abstract semi-linear evolution equation in a suitable Banach space for further study. Then the conditions Of the existence and uniqueness of the system solution are analyzed by using C0-semigroup theory.