Analysis of precision for maximum likelihood estimation in the Weibull distribution

Maximum likelihood estimation(MLE) in the Weibull distribution of parameters is considered an effective method, which is recommended in the case that the number of failure is more than 10 or equal 10. In practice, the number of failure is often less than 10 because of the high reliability or the fewness of sample. It is wanted to be known whether the MLE can be used in the case above; the number of failure, which makes the estimator have a given precision, will be known, sometimes, before the experimentation applying. So a method of analysis and estimation, which resolves that problems, was given with the idea of interval estimation. Then the precision of the estimator of shape parameter was discussed by this way under complete sample. In the practice projects, the precision of maximum likelihood estimation of Weibull shape parameter is quantitatively provided by the conclusion.