兰州大学机构库 >数学与统计学院
随机序及年龄概念在可靠性理论中的一些应用
Alternative TitleSome Applications of Stochastic Order and Aging Concepts in Reliability Theory
颜荣芳
Thesis Advisor李效虎
2009-05-22
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name博士
Keyword随机年龄概念 退化模型 超优序 比例失效率模型 冗余分配 随机序 随机占优序 强随机占优序 顺序统计量 样本间隔
Abstract随着社会的发展和科学技术的进步,系统的可靠性和安全性已成为现代工程设计中一个永恒的主题.随机序和随机变量的年龄性质因为在可靠性理论、系统安全、生存分析以及其它相关领域中的广泛应用也倍受应用概率统计界的关注.本文将进一步研究随机序和年龄性质在可靠性理论中的一些应用. 作为可靠性工程中的一项重要技术,贮备系统在最近二十多年以来一直是工程界和学术界关注的焦点.针对比例失效率元件组成的温贮备系统,我们引入了两个重要的系统评价指标,并通过两个指标进一步刻画了温贮备系统的可靠性. 同时,基于贮备成本最小化目标,我们建立了温贮备系统备用数量和备用时机的一个优化模型,得到了温贮备系统的最优备用数量和备用时机. 加速寿命检验以及退化模型是可靠性研究的重要问题之一. 从简单加性退化模型出发,我们进一步讨论了内在寿命的年龄性质与平均退化路径的分析性质及其随机变差的年龄性质之间的内在联系, 给出了内在寿命具有某些年龄性质的充分或必要条件.我们的结果还成功地修正了Bae et al.(2007)中的一些致命性错误. 顺序统计量与样本间隔在可靠性理论和寿命检验等诸多领域的研究中发挥着重要作用.基于观测量为随机变量的假设,我们讨论了单样本和双样本的顺序统计量和样本间隔的随机比较.我们还给出了样本量为随机变量的样本间隔随机比较的一些结果. 在文章的最后, 我们引入了强随机占优序的概念,剖析了强随机占优序与随机占优序以及普通随机序之间的关系,讨论了强随机占优序的性质, 并给出了它的等价刻画. 同时,我们应用强随机占优序进一步研究了元件的冗余分配问题.
Other AbstractThe reliability and safety of a system have become an eternal topic in modern engineering design with the social development and scientific and technological progress. Stochastic orders theory and aging concepts of random variables are also of great interest for having a wide application in such as reliability theory, system safety, survival analysis and other related areas. In this thesis, we will further investigate some applications of stochastic orders and aging concepts in reliability theory. As an important technology in reliability engineering, the standby system has been the focus of attention of both engineers and researchers in the recent two decades. Based on the warm standby system with components having proportional failure rates, we first introduce two important evaluation indices, which characterize the reliability of a warm standby system successfully. Furthermore, to minimize standby cost, we build an optimal model for a warm standby system in terms of standby number and standby time. The optimal standby number and standby time are also derived. The accelerated life testing and degradation model are one of the main topics in reliability theory. Based on the simple additive degradation model, the internal connection between the aging properties of the implied lifetime and the analytical properties of the mean degradation path and the aging properties of the random variation are discussed. The sufficient or necessary conditions for the implied lifetime with specified aging properties are also given. We thus successfully correct some serious mistakes in Bae et al.(2007). Order statistics and sample spacings play important roles in reliability theory, life testing and many other fields. We first conduct stochastic comparisons of order statistics and sample spacings from one sample and two samples when the number of observations is random. Meanwhile, when the sample size is random, the stochastic comparisons of sample spacings involved the usual stochastic order are also developed. At the end of this thesis, we introduce the strong stochastic precedence order. Relationships between strong stochastic precedence order and stochastic precedence order and usual stochastic order are discussed. We then present the properties of strong stochastic precedence order and establish its equivalent characterizations. In addition, we apply strong stochastic precedence order to further study the problem of the redundancy allocation of compo...
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/224654
Collection数学与统计学院
Recommended Citation
GB/T 7714
颜荣芳. 随机序及年龄概念在可靠性理论中的一些应用[D]. 兰州. 兰州大学,2009.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Altmetrics Score
Google Scholar
Similar articles in Google Scholar
[颜荣芳]'s Articles
Baidu academic
Similar articles in Baidu academic
[颜荣芳]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[颜荣芳]'s Articles
Terms of Use
No data!
Social Bookmark/Share
No comment.
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.