几类系统和元件剩余寿命与休止时间的随机性质

发布时间：2018-03-13 00:20

本文选题：剩余寿命　切入点：休止时间　出处：《兰州交通大学》2017年硕士论文　论文类型：学位论文

【摘要】：n中取k系统是一类非常重要的冗余系统,发展到现在已经在许多领域得到了广泛的应用.在现实生活中,一个系统中的元件具体到底是什么时候失效的,我们经常是不知道的,我们唯一可以确定的信息也许只有失效元件的总个数,所以一些学者开始关注系统的一般剩余寿命.当系统中元件的准确失效时间未知时,我们还可以把这个系统看作一个黑匣子.而休止时间表示从系统失效到观测这段时间,可用于尸体检验中.它还可以帮助可靠性工程师在合适的时间维修或者更换系统中的某些元件.在可靠性理论中,剩余寿命和休止时间都扮演着非常重要的角色.而对我们不确定的某些现象之间的比较经常用到随机比较理论.首先建立了n中取(n-k+1)系统的剩余寿命与休止时间模型,且组成这个系统的n个元件是独立同分布的.再利用条件概率公式给出该系统剩余寿命和休止时间的生存函数,通过对随机序知识的应用给出有关剩余寿命的几个随机比较,并得到系统的平均剩余寿命和平均休止时间.接着,我们考虑了n中取(n-q+1)系统(系统中的元件服从独立不同分布)一类新的休止时间,借助permanent得到该休止时间可靠度函数的混合表达式,并利用基本对称函数得到关于休止时间的几个定理.最后,我们给出了由n个相互独立元件构成的n中取k系统的剩余寿命与休止时间,分别在独立同分布和独立不同分布两种情况下对它们进行了讨论,得到其平均剩余寿命和平均休止时间,并给出剩余寿命的几个随机比较,当系统服从指数分布这种特殊分布时,对所得结论进行阐释.
[Abstract]:The k-in-n system is a very important redundant system, which has been widely used in many fields. We often don't know that the only information we can be sure of is probably only the total number of failure elements, so some scholars are beginning to focus on the general residual life of the system, when the exact failure time of the components in the system is unknown. We can also think of the system as a black box, and the interminable time means the time between the failure of the system and the period of observation. It can also help reliability engineers repair or replace certain components of the system at the right time. In reliability theory, The residual life and rest time play a very important role, and the random comparison theory is often used to compare some phenomena that we are not sure about. Firstly, the model of residual life and rest time of n-k 1) system in n is established. Moreover, n components of the system are independently distributed, and the survival functions of the residual life and rest time of the system are given by using the conditional probability formula, and several random comparisons about the residual life are given through the application of random order knowledge. The average residual life and mean rest time of the system are obtained. Then, we consider a new class of repose time of the system (the components in the system are distributed independently). By means of permanent, the mixed expression of the repose time reliability function is obtained, and some theorems about the rest time are obtained by using the basic symmetric function. In this paper, we give the residual life and rest time of k system in n, which is composed of n independent elements, and discuss them under the condition of independent same distribution and independent different distribution, respectively. The average residual life and the mean rest time are obtained, and several random comparisons of the residual life are given. When the system is distributed from the exponential distribution, the conclusion is explained.
【学位授予单位】：兰州交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O213.2

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