针对具有三种失效状态且修理延迟的单部件可修系统,以系统的第一种失效的次数$M$和第二种失效的次数$N$构造二元函数,以$(M,N)$为更换策略,运用(扩展)几何过程和更新过程的理论,推导出了系统的平均效益率的表达式$C(M,N)$和系统的平均可用率的表达式$A(M,N)$,在此基础上建立平均效益率和平均可用率的权衡优化模型.最后, 带入数值，运用Matlab软件,分析最优的$M^{\ast },N^{\ast }$.

In order to a repairable system consisting of one component with three types of failures and delayed repair, A function of two variables is structured by the first kind of failure times $M$ nd the second kinds of failure times $N$. Using $(M,N)$ as the replacement strategy and utilizing or spreading the geometric process and the theory of renewal process, the expression of the average profit rate $C(M,N)$ and the average availability rate $A(M,N)$ are calculated. Based on this, we have established the average profit rate and the average availability rate of the trade-off optimization model. Finally, using the Software Matlab,the optimal $M^{\ast },N^{\ast }$ are solved by a numerical example.