Reliability analysis of a one-unit system with finite vacations

This paper introduces finite vacations from a reliability theory viewpoint and deals with a one-unit repairable system with a repairman who takes finite vacations. A total probability decomposition method for analyzing the reliability problems of the system is presented with the help of the renewal process theory. With the decomposition method, two key reliability characteristics of the system i.e. the availability and mean failure number of the system are discussed under some assumptions. It is important that the steady-state availability and steady-state failure frequency of the system are obtained. Furthermore, three special cases of the model have showed that the vacation number taken by the repairman affects the performance of the system and the results presented in this paper are more general than the existing results in some literatures.