最佳无偏整体估计方法

提出一种最佳无偏整体估计方法,给出整体参数的估计量及其协方差公式,建立正态分布、Weibull分布和极值分布等位置-尺度分布族的点估计与区间估计。传统的回归分析只适用于正态分布和完全数据,最佳无偏整体估计方法则将回归分析推广到工程中常见的位置-尺度分布族和截尾数据的情况。该方法可以将不同条件(状态)下的试验数据作为一个整体进行统计推断,能够全面开发利用不同条件下试验数据之间的横向信息,使其可利用的信息量远远大于只能分别在各自条件下对试验数据进行处理的传统最佳线性无偏估计方法。最佳无偏整体估计方法对一种条件下只有一个失效数据的情况也能进行分析,传统最佳线性无偏估计方法则要求在一种条件下有较多的失效数据,因此前者具有小样本性质;并且前者的参数估计量是所有条件下顺序统计量的线性函数,后者的参数估计量只是一种条件下顺序统计量的线性函数,所以前者的参数估计量具有更好的正态分布特性。大量Monte Carlo模拟和工程应用表明,在试样数相同的情况下,文中方法比传统方法具有更高的精度,而在精度相同的情况下,则可节省大量试样。

BEST UNBIASED INTEGRAL ESTIMATE METHOD

A best unbiased integral estimate method is presented and the integral parameter estimators and their covariance are established. The point estimators and confidence intervals of normal distribution, Weibull distribution, extreme value distribution and other location scale parameter models are also given. The present method extends traditional regression analysis that is only suitable to complete data and normal distribution to censored data and the location scale parameter models that are common in engineering. As the crosswise information among the test data in different states is exploited and applied, the precision of the best unbiased integral estimate method is better than the traditional best linear unbiased estimate method. Furthermore the present method is applicable even when there is only one failure data while the traditional method requires more failure data, which shows the present method has the advantage of small sample. The parameter estimators obtained by the present method are the linear function of the order statistics in all states while those by the traditional method are the linear function of the order statistics in one state, thus the present estimators are more asymptotic to normal distribution than those by the traditional method. The present method has been applied in the reliability tests of aircraft and satellite successfully, and it shows that a great number of specimens can be saved.