LBS疲劳寿命分布的统计分析

发布时间：2018-12-28 10:41

【摘要】：Generalized Birnbaum-Saunders(GBS)分布是一种较为灵活的寿命模型,该模型在产品的可靠性分析中应用广泛,且拟合效果较优,因此探究此分布的性质,统计推断以及参数估计方法,成为具有理论价值和现实意义的课题。本文主要研究BS-Laplace(LBS)疲劳寿命分布。首先简单介绍了LBS分布的产生背景,对该分布的期望、方差、变异系数、相关系数、偏度、峰度等性质做了详细地推导计算,并分析了变量X-1和Xa(a0)的分布。然后,对密度函数、失效率函数及平均失效率函数的图像进行了研究,证明了它们的形状走势,并画出其在不同参数取值下的图像。得出该分布密度函数,失效率函数和平均失效率函数的形状均有两种:“倒浴盆形”和“倒浴盆-浴盆-倒浴盆形”。接着,给出了LBS分布中参数αβ,的几种估计方法,包括矩估计1、矩估计2、逆矩估计和分位数估计,并对以上几种估计方法做了综合比较,得出:四种方法下分位数估计对参数β的估计效果最好;矩估计2对参数α的估计效果最好;综合比较来说,分位数估计效果较好。其次,对LBS分布中的尺度参数β做了全样本下的区间估计,并对该区间估计进行了Monte Carlo模拟研究,结果表明该估计方法不太理想。再次,本文对LBS分布做了推广,引入位置参数μ,提出了三参数LBSIbam),,(疲劳寿命分布,并给出了参数的矩估计和分位数估计。此外,文中在给出LBSI分布参数真值情况下,模拟得出了两种方法下参数的估计值。
[Abstract]:The Generalized Birnbaum-Saunders (GBS) distribution is a flexible life model, which is widely used in the reliability analysis of products, and the fitting effect is better. Therefore, the properties of the distribution, statistical inference and parameter estimation methods are explored. It has become a topic of theoretical value and practical significance. The distribution of fatigue life of BS-Laplace (LBS) is studied in this paper. In this paper, the background of LBS distribution is introduced briefly. The properties of the distribution, such as expectation, variance, coefficient of variation, correlation coefficient, bias and kurtosis, are deduced and calculated in detail, and the distributions of variables X-1 and Xa (a0) are analyzed. Then, the images of density function, failure rate function and average failure rate function are studied, their shape trend is proved, and the images with different parameters are drawn. The distribution density function, the failure rate function and the average failure rate function have two shapes: "inverted bathtub shape" and "inverted bathtub-inverted bathtub shape". Then, several estimation methods of parameter 伪尾 in LBS distribution are given, including moment estimation 1, moment estimation 2, inverse moment estimation and quantile estimation. It is concluded that quantile estimation is the best method for parameter 尾 estimation. Moment estimation 2 has the best effect on parameter 伪, and the quantile estimation is better than other methods. Secondly, the interval estimation of the scale parameter 尾 in the LBS distribution is made under the whole sample, and the Monte Carlo simulation of the interval estimation is carried out. The results show that the estimation method is not very satisfactory. Thirdly, we generalize the LBS distribution, introduce the position parameter 渭, propose the three-parameter LBSIbam), (fatigue life distribution, and give the moment estimation and quantile estimation of the parameters. In addition, when the true values of LBSI distribution parameters are given, the estimated values of the two methods are obtained by simulation.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O213.2

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