Reliability Modeling for Repairable Systems With Stochastic Lifetimes and Uncertain Repair Times

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.