项目名称: 随机冲击环境下复杂系统可靠性的理论、方法与应用研究
项目编号: No.10871086
项目类型: 面上项目
立项/批准年度: 2009
项目学科: 金属学与金属工艺
项目作者: 李泽慧
作者单位: 兰州大学
项目金额: 23万元
中文摘要: 本项目进一步探索了随机冲击环境下复杂系统可靠性的研究框架、理论、方法和应用。主要研究了如下内容:提出了基于发射噪声过程框架下的累积冲击模型和局部累积冲击模型,并结合新风险模型研究了一类发射噪声过程在重尾分布下的精细大偏差和停时问题,得到了问题的解决途径;提出了截断δ#20914;击模型并获得了寿命分布结果,为管理科学中CLV的研究提供了数学基础;得到了δ#20914;击模型应用在维修理论中的进一步结果;获得了截断数据的最大似然估计结果。研究过程涉及到点过程、极限理论、生存分析等领域。在此起点上的探索,把累积冲击模型的研究提升到了与随机和的前沿领域相联系的水平上,并体现了概率与统计、可靠性与随机过程、理论与应用等相关领域的综合、交叉研究的特色。本项目的完成,不仅丰富了可靠性理论中的冲击模型研究的理论和方法,而且产生了相关随机过程的理论和方法;应用上也为描述和模拟相关系统的寿命现象提供了理论基础和方法。
中文关键词: 发射噪声过程;截断δ#20914;击模型;风险模型;重尾分布;极限理论
英文摘要: This project has explored further framework,theory and relevant methods for studying the reliability of complex systems under random shock enviromant, and also their applications. The main topics concerned are: - - -proposing and investigating the cumulative/loca-comulative shock model under the framework of cluster shot noise processes, especially, finding the proper approaches to research precise large deviation and stop time of a shot noise processes; - - -deriving theoretical of the censored δhock model,and then establish a mathematical basis for CLV-researching in manegement scleace; - - -exploring some new statistical approaches for the censored data; - - -combinig the results of theoretical study with simulation to promote the applications study in maintenance theory, new risk model and CLV. Stochastic processes, limit theory, survival analysis and other methods are involved in the study scheme. The study in this way has developed the shock model theory into a situation relating to the forward field of random sum, and has achieved the comprehensive feature of probability and statistics, reliability and stochastic processes, and theories and application. Such a research not only yields important value of reliability-studying, new theory and metholds for relative stochastic processes but also provides theoretical and methodological preparation for describing the lifetime of more extensive reliability systems.
英文关键词: Shot noise procces; Censored δhock model; Risk model; Heavy distribution: Limit theory