可靠性实验数据混合威布尔分布的参数优化估计

分别采用单一威布尔分布和多个威布尔分布组合的混合威布尔分布，对齿轮传动的可靠性实验数据进行了寿命分布描述。在用最大似然函数法对这两种分布进行分布参数的估计过程中，提出了一种通过最优化方法求得最大似然函数的新算法。通过对实验数据的计算，得出如下结论：该法的原理简单，方便实用；对带有折点的失效概率分布曲线，混合威布尔分布更能准确真实地反映实验数据的统计特性；该法可以推广到多于3个以上子分布组合的混合威布尔分布的参数估计。

Estimation of Parameter Optimization for Mixed Weibull Distributions from the Experimental Data of Reliability

In this paper, the single population Weibull distribution and the mixed Weibull distribution composed of many subpopulation Weibull distributions were adopted in describing the reliability test data of gears drive. In the process of estimating the distribution parameters of the two kinds of distributions by using the maximum likelihood method, a new algorithm for calculating the maximum value of the likelihood functions was developed based on the principle of the optimization. Through the calculation of the test data, the following conclusions were drawn: the concept of the algorithm is easy to be understood and applied; the mixed Weibull distribution is more suitable than the single population Weibull distribution when used for the failure probability distribution curve with break point; the algorithm can be used for the mixed Weibull distribution composed of more than three subpopulations Weibull distributions.