一类单部件可修复系统的稳定性及可靠性分析

The exponential stability and reliability analysis of a kind of single-component repairable system

研究了一类单部件可修复系统.首先利用补充变量法建立了模型,并证明了此系统的动态解以指数形式收敛于系统的稳态解,并且当修复率μ(x)为某一阶梯函数时,系统的瞬时可用度的极限不再是牢固可用度,并给出了此时系统可靠的条件.

A kind of single-component repairable system is investigated .We set up the model with supplemen-tary variable method ,and prove that the dynamic solution of the system exponentially converges to the steady-state solution .Moreover ,we prove that when the repair rate μ（x） is some piecewise function ,the limit of instant state availability is not the steady state availability of the system .Last ,we obtain the reliable condition of the system .