正态疲劳母体样本标准差的Weibull分布特征及应用

Weibull Distribution Features and Application of Sample Standard Deviation for Normal Fatigue Matrix

采用数值方法,研究了服从正态分布的总体在不同样本容量时其样本标准差的分布特征及变化规律,结果表明小子样条件下样本标准差呈偏态分布,具有Weibull分布的特征。利用三参数Weibull分布归纳出分布参数的数学模型,进而提出了一种具有更高精度的小子样总体标准差区间估计方法,并得到试验数据的验证。

A computer simulation has been made to study the statistical distribution features of sample standard deviation in different sampling sizes under the normal distribution matrix. The results and their analysis show that the distribution of sample standard deviation appears a skewness which has the same characteristics as Weibull distribution in small scale samples. Then,a stochastic model based on three-parameter Weibull distribution is generalized to describe the distribution parameters. Furthermore, an interval estimating method with higher accuracy which is verified by experimental data,is proposed for the overall standard deviation of small scale samples in reliability analysis.