The Fiducial Inference for Repaired as Old Weibull Distributed Systems

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.