Abstract: For Weibull distributed systems, one kind of repaired as old model is considered, and the availability function in any time is derived respectively for the maintainance time is a constant or is a discrete r.v.; Based on the complete-data in life testing, a Fiducial distribution is given to the the reliability function, furthermore, the point estimation and the lower bound confidence estimation are derived. A monte carlo result is given in the end, and it shows that, in the small sample situation (n＜10), the estimation to the lower bound confidence is ok but not steady; when the sample size is more than 15, a more accurate inference can be drawn.