In actual industrial systems, there are often situations where the fault data are sufficient, whereas the repair data are insufficient. It is not appropriate to treat the system as a stochastic system or an uncertain system in this case. In this paper, the lifetimes of components are assumed to be random variables and the repair times of components are assumed to be uncertain variables. The entire system can be regarded as an uncertain random repairable system accordingly. Based on chance theory, some common reliability indexes of repairable system, such as availability, steady-state failure frequency, mean up time, and mean down time, are redefined and some properties are also presented. Then, the reliability mathematical models of repairable series systems, repairable parallel systems, repairable series-parallel systems, and repairable parallel-series systems are established, respectively. Furthermore, the formulas of reliability indexes of each repairable system are obtained. Finally, some numerical examples are presented to illustrate the calculation of the reliability indexes.

中文翻译：

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具有随机寿命和不确定修复时间的可修复系统的可靠性建模

在实际的工业系统中，经常会出现故障数据充足而修复数据不足的情况。在这种情况下，将系统视为随机系统或不确定系统是不合适的。在本文中，假设部件的寿命是随机变量，部件的修复时间被假设为不确定变量。相应地，整个系统可视为一个不确定的随机可修复系统。基于机会理论，重新定义了可修复系统的一些常见可靠性指标，如可用性、稳态故障频率、平均正常运行时间和平均停机时间，并给出了一些特性。然后，可修串联系统、可修并联系统、可修串并联系统的可靠性数学模型，和可修复的并联串联系统分别建立。进而得到各可修系统的可靠性指标公式。最后，给出了一些数值例子来说明可靠性指标的计算。