三参数威布尔形状参数估计方法的比较与推荐取值

Comparison of Three-parameter Weibull Shape Parameter Estimation Methods and Its Recommended Values

机电产品寿命大多数服从威布尔分布,其形状参数与潜在的失效机制有关,在相似环境下运行的产品的寿命概率分布通常有大致相同的形状参数。然而,目前在许多实际应用中威布尔形状参数值的范围和取值是基于两参数威布尔分布估计得到,这使得威布尔形状参数范围出现了较为分散的现象。首先使用偏差和方均根误差两个统计特征比较三参数威布尔形状参数估计的相关系数法、最小二乘法和最小偏差法。通过蒙特卡洛仿真验证,表明了相关系数法估计的形状参数更加准确。收集文献中的疲劳试验数据和其他机电产品寿命数据均使用两参数威布尔分布、三参数威布尔分布和对数正态分布进行拟合并通过K-S检验,通过比较三种分布的D值,说明三参数威布尔分布拟合效果最好。使用相关系数法得到三参数威布尔分布形状参数的取值和范围,计算结果表明机电产品的形状参数范围为1.0~3.0,均值为1.774。

The shape parameters of Weibull distribution of electromechanical products are related to potential failure mechanisms,and the life probability distributions of products operating in similar environments usually have approximately the same shape parameters.However,the ranges and values of the Weibull shape parameter values in many practical applications are currently obtained based on the two-parameter Weibull distribution estimates,which makes the Weibull shape parameter ranges appear more scattered.Correlation coefficient method is compared with least squares method,and minimum discrepancy method for the estimation of the three-parameter Weibull shape parameter by two statistical features that are bias and root mean square error.Validation by Monte Carlo simulation shows that the correlation coefficient is more accurate.The fatigue test data and other electromechanical product life data collected in the literatures are fitted by the two-parameter Weibull distribution,the three-parameter Weibull distribution and the lognormal distribution and pass the K-S test.By comparing D-values of the three distributions,it is shown that the three-parameter Weibull distribution fits best.The correlation coefficient method is used to obtain the values and ranges of the shape parameters of the three-parameter Weibull distributeon.The calculation results show that the range of shape parameters of electromechanical products is 1.0-3.0,and the mean value is 1.774.