Reliability Mathematical Models of Repairable Systems With Uncertain Lifetimes and Repair Times

In system reliability problems, the lifetimes and the repair times are usually indeterministic. When insufficient samples are available to estimate distribution functions of the lifetimes and the repair times, it is rational to invite some experts to evaluate the belief degrees. Uncertainty theory is a branch of mathematics for modelling belief degrees. In this paper, the lifetimes and the repair times of typical repairable systems are assumed to be uncertain variables. Based on the above-mentioned assumptions, the uncertain reliability mathematical models of simple repairable series systems, simple repairable parallel systems, simple repairable series-parallel systems, and simple repairable parallel–series systems are established, respectively. The reliability indices, such as steady state availability, steady state failure frequency, mean up time, and mean down time, are proposed. Finally, some numerical examples are given for illustration.