【作者】 刘冬雪；

【导师】 刘颖；

【作者基本信息】 天津科技大学 ， 计算机应用技术， 2019， 硕士

【摘要】 冲击模型是可靠性理论的重要组成部分,一般用来对非确定环境下系统的生存、失败及维修等现象进行建模。在研究冲击模型建模的过程中不得不面对各种非确定性因素,包括随机性、不确定性以及随机性与不确定性并存的情况。通常对冲击模型的研究只局限于概率模型,但是以概率论为数学工具对系统进行建模需满足三个基本前提,即事件需明确定义、有大量样本存在以及样本之间具有概率重复性。当没有足够样本来估计概率分布时,我们只能依靠专家的主观信度去评估事件发生的可能性,而不确定理论是用来处理主观信度的数学分支。本文针对不确定情形以及不确定和随机并存的情形分别对冲击模型进行建模和分析,主要研究工作如下:当冲击模型无大量的样本存在时,运用不确定理论对冲击模型进行建模分析。假设系统由两个部件组成且环境中有三个相互独立的冲击源,每个冲击到达均引起部件失效且失效的时间为不确定变量,在此基础上建立致命冲击数学模型并进行分析,给出两部件寿命的联合生存不确定分布、矩的相关公式和矩母函数等结论。在实际问题中,通常存在不确定性和随机性并存的情形,此时需采用机会理论对冲击模型进行建模和分析。假设系统由两个部件组成且环境中有六个相互独立的冲击源且冲击源包括两种类型,一种是有大量统计数据支持的冲击源,即视为随机情形;另一种是无大量统计数据支撑的冲击源,即视为不确定情形。每个冲击到达均会引起部件失效,则失效时间为不确定随机变量,利用机会理论为数学工具建立了致命冲击模型的数学模型,并对模型进行了分析。给出了两部件寿命的联合生存机会分布及相关定理。此研究工作为可靠性数学相关领域的发展提供了新的建模方法,不仅具有重要的学术意义,而且还具有广泛的实用价值和应用前景。更多还原

【Abstract】 The shock model is an important part of the reliability theory and is generally used to model the survival,failure and maintenance of systems in non-deterministic environments.However,in the process of studying the shock model,we have to face all kinds of non-deterministic factors,including the phenomenon of randomness,uncertainty and the coexistence of randomness and uncertainty.Although probability theory is an effective mathematical tool to study this non-determinism.Using probability theory to deal with engineering problems depends on three premises:the clearly defined event,a large number of samples and probability of repeatability among the samples.When the above conditions are not met at the same time,the probability theory cannot be used.When no samples are available to estimate a probability distribution,we usually invite some domain experts to evaluate the belief degree that each event will happen.The uncertainty theory is the mathematical branch used to deal with subjective reliability.Therefore,in this paper,the shock model is modeled and analyzed separately for uncertain situations and uncertain and random coexistence situations,mainly doing the following research:When the shock model does not have a large number of samples,the shock model is modeled and analyzed by using uncertainty theory.Assume that the system is composed of two components and it has three independent shock sources.We also assume that the shock sources leading to failure for components and the failure times are uncertain.Based on that,the fatal shock model is established and analyzed.Furthermore,the joint survival uncertainty distribution for the lifetimes of the two components and some basic theorems are arrived,respectively.Finally,some numerical examples are given.In actual fatal shock models analysis,there has both random and uncertain factors.Under uncertain random environment,it is assumed that the system is composed of two components and has six independent shock sources.There are two major types of shock sources in this system,one type of shock source is supported by statistical data,and the other one is supported by expert experience.The chance theory is introduced into the study of the fatal shock models.Based on that,the fatal shock model under uncertain random environment is established.The joint survival chance distribution for the lifetimes of the two components and some basic theorems are presented.Finally,some numerical examples are given.The paper provides a new modeling method for the development of reliability mathematics and related fields.It not only has academic significance,but also has practical value and broad application prospects.更多还原