威布尔分布多元回归分析方法

提出威布尔分布多元回归分析方法,建立回归参数的最佳无偏整体估计及其协方差公式,给出威布尔分布、极值分布和正态分布的百分位值(如可靠寿命和安全强度)的置信限估计。传统的多元回归分析只适用于正态分布和完全数据的情况,而本文则将其推广到威布尔分布、极值分布和截尾数据的情况。与传统的成组试验和最佳线性无偏估计方法相比,本文方法可以将不同条件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,在试样数相同的情况下,具有更高的估计精度,而在精度相同的条件下,则可以节省大量试样。

Multiple Regression Analysis Method for Weibull Distribution

A new multiple regression analysis method for Weibull distribution and extreme distribution is presented. The best unbiased integral estimation for regression parameters and their covariance are established by the method. The point estimators and confidence intervals of Weibull distribution, extreme distribution and normal distribution are also given. The present method extends the traditional multiple regression analysis that is only suitable to normal distribution and complete data to Weibull distribution, extreme distribution and censored data. Compared with the traditional group test method and best linear unbiased estimation, the present method can fully exploit and apply the crosswise information among the test data in different states; thus it reaches a better precision and a great number of specimens can be saved.