威布尔分布的极大似然估计的精度分析

威布尔分布参数估计的极大似然方法是一种常用的方法,在故障数不小于10的情况下推荐使用.但在工程中,由于产品的可靠性高,或者是样本量少,试验的故障数常常是小于10,在这种情况下需要明确所得的评估结果的精度是否满足要求.运用区间估计的思想,提出了一种解决上述问题的评价和判断的方法,并应用此方法对完全样本情况下,形状参数的极大似然估计量的精度进行了讨论.工程上,可以依据文中提供的结论定量分析威布尔分布形状参数极大似然估计量的精度.

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.