几类更新截断δ冲击模型的参数估计

发布时间：2018-01-12 08:03

本文关键词：几类更新截断δ冲击模型的参数估计　出处：《西北民族大学》2016年硕士论文　论文类型：学位论文

【摘要】：可靠性理论自20世纪30年代提出以来,一直是复杂系统和设备领域研究的重点,可靠性理论的核心内容是系统寿命预测,准确的预测系统寿命对于经济活动有着重要的作用。有关可靠性的数学模型比较多,其中截断δ冲击模型是可靠性模型的一种。本文讨论了截断δ冲击模型中参数的估计量问题,主要包括两部分内容。第一部分,针对单样本情形,讨论了更新冲击间隔下截断δ冲击模型的参数估计问题。对于每一种特殊分布,应用三种估计方法：极大似然估计、信息先验分布的Bayes估计和无信息先验分布的Bayes估计来得到对应方法的参数估计量,并且得到了参数估计量的期望。进而借助MATLAB R2013对三种估计方法得到的参数估计量进行了数值模拟,从而得出每一种特殊分布下三种方法的选取方案。在研究了特殊分布之后,更深入地推广到了一般分布上,同样得到了三种估计方法下的估计量和期望。第二部分,针对多样本情形,除了分别讨论每种特殊分布下三种估计方法的估计量和期望,还讨论了参数极大似然估计量的分布函数和相合性。最后,在一般分布函数下研究了同样的问题。本文利用参数估计的方法对不同分布下的参数进行估计并给出了对应分布下参数估计方法的选取建议,这对于完善可靠性系统理论具有极其重要的作用。
[Abstract]:Since 1930s, the reliability theory has been the focus of research in the field of complex systems and equipment. The core of reliability theory is system life prediction. Accurate prediction of system life plays an important role in economic activities. There are many mathematical models about reliability. The truncated 未 impact model is one of the reliability models. This paper discusses the estimation of parameters in the truncated 未 impact model, which consists of two parts. The first part is for a single sample case. This paper discusses the parameter estimation of truncated 未 -impact model with renewed shock interval. For each special distribution, three estimation methods are applied: maximum likelihood estimation. The Bayes estimation of the information prior distribution and the Bayes estimation of the uninformed prior distribution are used to obtain the parameter estimator of the corresponding method. The expectation of the parameter estimator is obtained, and then the numerical simulation of the parameter estimator obtained by the three methods is carried out with the help of MATLAB R2013. The selection scheme of three methods under each special distribution is obtained. After studying the special distribution, it is further extended to the general distribution. In the second part, we discuss the estimator and expectation of the three estimation methods under each special distribution except for the case of multiple samples. The distribution function and consistency of the parameter maximum likelihood estimator are also discussed. The same problem is studied under the general distribution function. In this paper, the parameter estimation method is used to estimate the parameters under different distributions and the selection suggestions of the parameter estimation methods under the corresponding distribution are given. It is very important to perfect the theory of reliability system.
【学位授予单位】：西北民族大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O212.1

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