【作者】 赵雯晖；

【导师】 张国志；

【作者基本信息】 哈尔滨理工大学 ， 应用数学， 2011， 硕士

【摘要】 可靠性数学理论起源于20世纪30年代,最早被应用的领域是机械证明,维修问题。另一个重要应用是将更新问题应用于更换问题。在30年代,威布尔,龚贝尔和爱泼斯坦等人研究了材料的疲劳寿命以及相关的极值问题。在二次世界大战以后,可靠性问题得到了更大的重视,随着在军事技术装备上的应用日新月异,可靠性问题也更多的应用到生活中随处可见的复杂系统问题上。从50年代至今,可靠性这门新兴的学科以惊人的速度发展着,在各个领域都积累了丰富的经验,可靠性理论的应用已经从军事技术领域扩展到了国民经济等许多领域。系统的可靠度,平均寿命,子系统的重要度等都是评估系统可靠性的重要指标,在航天航空等领域,相对于其他指标,平均寿命有其独特的意义。目前,系统的平均寿命在日常生活中的应用也越来越被重视。本文主要研究以下几个问题:首先,了解复杂系统的基本知识要点,描述复杂系统的方法,介绍了最小路径矩阵和最小割集矩阵的定义以及可靠度的解析表达式等相关理论知识。其次,对子系统寿命变量分布服从指数分布的复杂系统,利用可靠度的解析表达式,给出了系统平均寿命的表达形式。进一步分别在完全数据和截尾数据两种情况下,给出了其估计,并在完全数据形式下,证明了其估计的渐近正态性。最后,对于子系统寿命变量服从一般分布的情况下,给出了系统平均寿命的估计,并对估计性质进行了研究。更多还原

【Abstract】 The theory of mathematical reliability dated from 1930’s which had been used in the area of mechanical proof and maintenance at the very beginning. Another important application of this theory was to apply the question of updating to the question of replacement. In 1930’s, the pioneers, Weibull, Gong Bell and Epstein, had done the research about the fatigue life of materials and the relative problem of extremum. After the World WarⅡ, the question of reliability had been focused more, and this question was used to solve the systematic problems in daily life as the improvement of military technology. since 1950’s, the subject of reliability has been developing rapidly and getting rich experiences in different areas. The application of reliability theory is now extends from military technology to all areas of national economy.The reliability, mean life, importance of the subsystem are the essential indicators of system reliability evaluating, but in the region of aerospace we focus on mean life more than any other indicators. Now, the life expectancy of the system has been taken more serious in everyday life.Several questions had been investigated as follows:Firstly, intrducting the basic knowledge of the complex system and the methods for describing complex system, which also introduce the conception of minimum path matrix and minimal cut set matrix as well as the relative theory about the analytical expression of reliability.Secondly, for the complex system whose every subsystem life having exponential distribution, the mean life of it is given by using function of complex system reliability. Estimation of the system mean life are presented under complete datum as well as censored datum. Furthermore, we prove the asymptotic normality of complex system reliability under complete datum condition.At last, for the complex system whose every subsystem life having general distribution, the estimation of the complex system is given and the properties are studied.更多还原