二参数威布尔分布最小二乘法估计的优化研究

A Refine Study on the Least-Squares Estimation for Two-Parameter Weibull Distribution

摘要: 威布尔分布是可靠性科学和工程中常用的随机变量分布之一。将具有威布尔分布的非线性可靠度函数对数线性化，可方便威布尔参数的求解，但却降低了参数估计的精度。针对这个问题，提出了应用泰勒级数展开结合最小二乘法提高威布尔分布的拟合精度。通过数值模拟和实例计算，对比分析了泰勒级数展开–最小二乘法与普通最小二乘法及其加权处理的拟合效果。结果表明，该方法可以有效降低威布尔曲线拟合的误差，为可靠性试验提供参考。

Abstract: Weibull distribution is one of the common random variable distributions in reliability science and engineering. Despite the fact that log-linearizing the nonlinear reliability function with Weibull distribution contributes to solving the Weibull parameters, the precision of parameter estimation is reduced. Thus, a method by combining Taylor series expansion and least square method is pro-posed to improve fitting precision of the Weibull distribution. Contrastive analyses on Taylor series expansion-least square method, common least square method and weighted least square method are conducted to access the fitting effects via numerical simulation and calculation. The results show that the proposed method can reduce the Weibull curve fitting error effectively and thus can be reference for reliability test.