基广义指数分布的应力强度模型可靠度的估计

发布时间：2018-02-17 04:18

本文关键词： 广义指数分布应力强度模型可靠度广义估计广义置信区间 bootstrap置信区间　出处：《浙江工商大学》2017年硕士论文　论文类型：学位论文

【摘要】：应力强度模型自从正式提出来以后,许多数学、统计与工程学的研究者分别加入了该模型的研究。从统计学角度,我们可以从参数和非参两种方法去研究该模型,模型的主要应用范围有工程机械领域、桥梁工程领域等。由于现实生活对产品及零件可靠度的要求很高,所以迫使人们为此做出大量研究。广义指数分布(GED)是1999年Gupta和Kundu基于指数分布的基础上提出的,并对该分布做了大量研究。广义指数分布是寿命分布的一种,许多学者都对其做了研究,本文我们将该分布应用到应力强度模型上,并对应力强度模型做出了参数估计。本文主要研究了当随机变量应力X和强度y独立且服从广义指数分布时,可靠度的统计推断问题。我们分布考虑了尺度参数相等、形状参数相等和都不等三种情况下,应力强度模型可靠度的点估计和区间估计问题。我们通过计算分别得出了这三种情况下,可靠度的最大似然估计值和广义估计值。然后通过Monte Carlo模拟获得可靠度估计值的相对偏差和相对均方误差,发现广义估计对可靠度的点估计效果更好。对于区间估计,我们用可靠度的90%和95%分位数模拟可靠度的区间估计,得出在样本容量较少时,广义置信区间的模拟覆盖率与名义覆盖率基本一致。但基于最大似然估计的Bootstrap分位数置信区间的模拟覆盖率与名义覆盖率相差较大。
[Abstract]:Since the formal introduction of the stress intensity model, many researchers in mathematics, statistics and engineering have joined in the study of the model. From a statistical point of view, we can study the model in terms of both parametric and non-parametric methods. The main applications of the model are in the field of construction machinery, bridge engineering and so on. In 1999, Gupta and Kundu put forward on the basis of exponential distribution, and did a lot of research on this distribution. The generalized exponential distribution is a kind of life distribution. In this paper, we apply this distribution to the stress intensity model. In this paper, we mainly study the statistical inference of reliability when the stress X and strength y of random variables are independent and from the generalized exponential distribution. The problem of point estimation and interval estimation of the reliability of stress intensity model is obtained under the condition of equal shape parameters and unequal shape parameters. The maximum likelihood and generalized estimators of reliability are obtained by Monte Carlo simulation, and the relative deviation and mean square error of reliability estimates are obtained. It is found that generalized estimators are more effective for point estimation of reliability. We use the 90% and 95 quartiles of the reliability to simulate the interval estimation of the reliability, and we get that when the sample size is small, The simulated coverage of the generalized confidence interval is basically the same as the nominal coverage, but the simulated coverage of the confidence interval of Bootstrap quantiles based on the maximum likelihood estimation is quite different from that of the nominal coverage.
【学位授予单位】：浙江工商大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：C813

【相似文献】