Geometric process analysis of a two-unit series system with repairman vacation

This paper studies a two-dissimilar-unit series system with single repairman vacation. It is assumed that the working time of the two units obeys exponential distributions, and the repair time and the vacation time obey general distributions. And it is also assumed that unit 2 after repair is as good as new while unit 1 after repair is not. By using geometric process, the method of supplementary variable and Laplace transform, some main reliability indices of the system are obtained which contain the availability, the reliability and the asymptotic failure frequency of the system, along with the idle and the off probability of the repairman.