基于混合Gamma分布的通用可靠性寿命数据拟合方法

 可靠性寿命数据分析是可靠性工程研究的重要基础。目前对于可靠性寿命数据分析的研究存在两个主要问题:一是凭经验选择的概率分布严重依赖于人的主观判断,不能保证所选分布的适用性；二是常用分布拟合能力有限,在很多情况下不能满足寿命数据处理的需要。针对这两个问题，在混合Gamma分布稠密性的基础上，提出了一种通用的可靠性寿命数据拟合方法，给出了基于期望极大化(EM)算法的混合Gamma分布的参数估计方法，并通过6个拟合实例验证了该方法的有效性。最后，结合WP-7乙型航空发动机I级导叶片故障数据分析问题，开展了应用研究，并且与目前常用的方法进行了对比。

General Reliability Life Data Fit Method Based on Mixture of Gamma Distributions

The reliability life data analysis is an important basis of reliability engineering.Two main problems are still unsolved in this field: one is that the probability distribution selected by experience depends heavily on the people's subject judgment,and so can not ensure its applicability;the other is that the usual probability distributions can not meet the need of life time data fit in many instances because their fit abilities are limited.To solve the two problems,firstly this paper gives the denseness proof of the proposed Gamma mixture.Secondly,a general reliability life data fit method,which is based on the denseness of Gamma mixture,is proposed.For the Gamma mixture parameter estimation,an algorithm of expectation maximization(EM) type is developed.To illustrate the effectiveness of the method proposed,six examples are used.Finally,the WP-7 aviation engine's I-class blade failure data analysis is taken as the application example to compare the proposed method with the conventional ones.