广义推断在系统可靠性问题中的应用
发布时间：2019-04-25 20:14
【摘要】：广义推断是基于广义检验变量或广义枢轴量的统计推断方法,由广义置信区间估计和广义p值检验组成.它的提出是为了解决小样本中存在讨厌参数的统计推断问题,而这恰是经典频率学中的方法有时候也无法给出相应的较好解决方案的问题.系统可靠性的统计推断是现代社会发展中不可忽视的重要问题,尤其是在工业农业各个生产线以及高新科技产业等复杂、高风险的系统中.然而,大多数学者都只是针对个别分布做了可靠性问题的广义推断,且仅仅给出了数据模拟结果,并未给出相应的频率性质的证明.同时,用广义推断来研究系统可靠性问题的文章也很少.鉴于此,本学位论文的主要研究工作如下:1.研究了含有多个元件的串联系统的可靠性问题的广义推断.分别在平衡与不平衡状态下通过枢轴方程构造出了可靠性函数的广义枢轴量,进而给出了广义p值与广义置信区间.并且相应的给出在对数正态分布、指数分布、Weibull分布下的结果.分别证明了小样本与大样本定理,说明了其犯第一类错误的概率接近于名义水平.最后,采取了蒙特卡罗模拟方法对我们所研究的问题做出了数据模拟,其结果显示广义推断方法在小样本且含讨厌参数的串联系统可靠性问题中表现优秀.2.给出了含有多个元件的并联系统的可靠性问题的广义推断.通过枢轴方程给出了可靠性函数的广义枢轴量.并联系统当中,本文直接在不平衡状态下给出了可靠性函数的广义p值以及广义置信区间,并分别给出了三种不同分布下的结果,即对数正态分布、指数分布、Weibull分布.相应的证明了大样本以及小样本定理,说明其犯第一类错误的概率趋近于名义水平.最后通过蒙特卡罗模拟方法给出了犯第一类错误的概率、置信区间与平均长度,有力地证明了广义推断方法在小样本并联系统可靠性问题中有着良好的应用.3.在前两部分的基础之上,本文将可靠性问题的广义推断方法推广到了包含m个串联元件和m个并联元件的混合系统当中.直接给出了不平衡状态时对数正态分布、指数分布、Weibull分布下的可靠性函数的假设检验与置信区间.同样,给出了小样本与大样本定理的证明,说明其犯第一类错误的概率趋近于名义水平.最后,通过蒙特卡罗模拟方法给出了犯第一类错误的概率、置信区间及其平均长度.从结果可以看出,广义推断方法在小样本混合系统可靠性问题中有着优秀表现.
[Abstract]:Generalized inference is a statistical inference method based on generalized test variables or generalized pivot variables. It consists of generalized confidence interval estimates and generalized p-value tests. It is proposed in order to solve the problem of statistical inference of unwanted parameters in small samples, and this is the problem that the classical frequency method sometimes can not give the corresponding better solutions. The statistical inference of system reliability is an important problem that can not be ignored in the development of modern society, especially in the complex and high-risk systems such as industrial agricultural production lines, high-tech industries and other complex and high-tech industries. However, most scholars have only made the generalized inference for the reliability of individual distributions, and only given the results of data simulation, and did not give the corresponding proof of the frequency properties. At the same time, there are few papers using generalized inference to study the problem of system reliability. In view of this, the main research work of this dissertation is as follows: 1. In this paper, the generalized inference of reliability problem for series systems with multiple components is studied. The generalized pivot quantity of reliability function is constructed by the pivot equation in the equilibrium and unbalanced states, and then the generalized p-value and the generalized confidence interval are given. The corresponding results under logarithmic normal distribution, exponential distribution and Weibull distribution are given. We prove the theorems of small sample and large sample respectively, and show that the probability of making the first kind of error is close to the nominal level. Finally, the Monte Carlo simulation method is used to simulate the problems we have studied. The results show that the generalized inference method performs well in the reliability problems of series systems with small samples and hateful parameters. 2. In this paper, the generalized inference of reliability problem for parallel systems with multiple components is given. The generalized pivot quantity of reliability function is given by the pivot equation. In parallel systems, the generalized p-value and the generalized confidence interval of the reliability function are given directly in the unbalanced state, and the results under three different distributions are given, namely the logarithmic normal distribution, the exponential distribution and the Weibull distribution. The corresponding theorems of large samples and small samples are proved, which shows that the probability of making the first kind of errors tends to be close to the nominal level. Finally, the probability, confidence interval and average length of the first kind of errors are given by Monte Carlo simulation method. It is proved that the generalized inference method has a good application in the reliability problem of small sample parallel systems. On the basis of the first two parts, the generalized inference method of reliability problem is extended to the hybrid system with m series elements and m parallel elements. The hypothesis test and confidence interval of reliability function under the conditions of logarithmic normal distribution, exponential distribution and Weibull distribution are given directly. In the same way, the proof of small sample theorem and large sample theorem is given, which shows that the probability of making the first kind of error is close to the nominal level. Finally, the probability, confidence interval and average length of making the first kind of error are given by Monte Carlo simulation method. It can be seen from the results that the generalized inference method has excellent performance in the reliability problem of small sample hybrid systems.
【学位授予单位】：北京建筑大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O213.2
本文编号：2465426
[Abstract]:Generalized inference is a statistical inference method based on generalized test variables or generalized pivot variables. It consists of generalized confidence interval estimates and generalized p-value tests. It is proposed in order to solve the problem of statistical inference of unwanted parameters in small samples, and this is the problem that the classical frequency method sometimes can not give the corresponding better solutions. The statistical inference of system reliability is an important problem that can not be ignored in the development of modern society, especially in the complex and high-risk systems such as industrial agricultural production lines, high-tech industries and other complex and high-tech industries. However, most scholars have only made the generalized inference for the reliability of individual distributions, and only given the results of data simulation, and did not give the corresponding proof of the frequency properties. At the same time, there are few papers using generalized inference to study the problem of system reliability. In view of this, the main research work of this dissertation is as follows: 1. In this paper, the generalized inference of reliability problem for series systems with multiple components is studied. The generalized pivot quantity of reliability function is constructed by the pivot equation in the equilibrium and unbalanced states, and then the generalized p-value and the generalized confidence interval are given. The corresponding results under logarithmic normal distribution, exponential distribution and Weibull distribution are given. We prove the theorems of small sample and large sample respectively, and show that the probability of making the first kind of error is close to the nominal level. Finally, the Monte Carlo simulation method is used to simulate the problems we have studied. The results show that the generalized inference method performs well in the reliability problems of series systems with small samples and hateful parameters. 2. In this paper, the generalized inference of reliability problem for parallel systems with multiple components is given. The generalized pivot quantity of reliability function is given by the pivot equation. In parallel systems, the generalized p-value and the generalized confidence interval of the reliability function are given directly in the unbalanced state, and the results under three different distributions are given, namely the logarithmic normal distribution, the exponential distribution and the Weibull distribution. The corresponding theorems of large samples and small samples are proved, which shows that the probability of making the first kind of errors tends to be close to the nominal level. Finally, the probability, confidence interval and average length of the first kind of errors are given by Monte Carlo simulation method. It is proved that the generalized inference method has a good application in the reliability problem of small sample parallel systems. On the basis of the first two parts, the generalized inference method of reliability problem is extended to the hybrid system with m series elements and m parallel elements. The hypothesis test and confidence interval of reliability function under the conditions of logarithmic normal distribution, exponential distribution and Weibull distribution are given directly. In the same way, the proof of small sample theorem and large sample theorem is given, which shows that the probability of making the first kind of error is close to the nominal level. Finally, the probability, confidence interval and average length of making the first kind of error are given by Monte Carlo simulation method. It can be seen from the results that the generalized inference method has excellent performance in the reliability problem of small sample hybrid systems.
【学位授予单位】：北京建筑大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O213.2
【参考文献】
相关期刊论文 前3条
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3 ;GENERALIZED CONFIDENCE REGIONS OF FIXED EFFECTS IN THE TWO-WAY ANOVA[J];Journal of Systems Science and Complexity;2008年02期
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