Stress‐Strength Reliability Analysis with Extreme Values based on q‐Exponential Distribution
Stress‐Strength Reliability Analysis with Extreme Values based on q‐Exponential Distribution
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DOI：
10.1002/qre.2020
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发表时间：
2017-04
影响因子：
2.3
通讯作者：
Romero Sales Filho;E. Droguett;I. Lins;M. Moura;M. Amiri;R. Azevedo
中科院分区：
文献类型：
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作者：
Romero Sales Filho;E. Droguett;I. Lins;M. Moura;M. Amiri;R. Azevedo
在处理应力-强度可靠性的实际问题时，可以使用疲劳寿命数据并利用应力与失效循环之间众所周知的关系。对于某些材料，此类数据可能涉及极大的值。在此背景下，本文讨论了估计应力-强度可靠性的可靠性指数 R = P(Y < X) 的问题，其中应力 Y 和强度 X 是独立的 q 指数随机变量。此选择基于 q 指数分布对具有极大值的数据进行建模的能力。我们开发了指数 R 的最大似然估计器，并通过模拟实验分析其行为。此外，置信区间是基于参数和非参数引导程序开发的。所提出的方法适用于涉及实验数据的两个案例研究：第一个案例与球墨铸铁的高周疲劳分析有关，而第二个案例则评估了样本尺寸对高强度钢的十周疲劳性能的影响。提供了两个案例研究的 q 指数分布的充分性以及基于指数 R 的最大似然估计的点和区间估计。 q 指数分布与威布尔分布和指数分布之间的比较表明，q 指数分布在拟合应力和强度实验数据以及估计的 R 指数方面呈现出更好的结果。版权所有 © 2016 约翰威利父子有限公司
When dealing with practical problems of stress–strength reliability, one can work with fatigue life data and make use of the well‐known relation between stress and cycles until failure. For some materials, this kind of data can involve extremely large values. In this context, this paper discusses the problem of estimating the reliability index R = P(Y < X) for stress–strength reliability, where stress Y and strength X are independent q‐exponential random variables. This choice is based on the q‐exponential distribution's capability to model data with extremely large values. We develop the maximum likelihood estimator for the index R and analyze its behavior by means of simulated experiments. Moreover, confidence intervals are developed based on parametric and nonparametric bootstrap. The proposed approach is applied to two case studies involving experimental data: The first one is related to the analysis of high‐cycle fatigue of ductile cast iron, whereas the second one evaluates the specimen size effects on gigacycle fatigue properties of high‐strength steel. The adequacy of the q‐exponential distribution for both case studies and the point and interval estimates based on maximum likelihood estimator of the index R are provided. A comparison between the q‐exponential and both Weibull and exponential distributions shows that the q‐exponential distribution presents better results for fitting both stress and strength experimental data as well as for the estimated R index. Copyright © 2016 John Wiley & Sons, Ltd.