含桥联复杂系统的Bayes可靠性分析及Bayes统计决策问题中的几个结论

【作者】 常宝娴；

【导师】 刘力维；

【作者基本信息】 南京理工大学 ， 运筹学与控制论， 2006， 硕士

【摘要】 本文由独立的两部分组成。 第一部分研究了含桥联复杂系统的Bayes可靠性问题。 本文在分析现有研究的基础上，借鉴了已有的复杂系统可靠性的Bayes分析方法，研究了串联系统的可靠性，并从统计学的角度研究了新的模型——桥联系统、串—桥联系统以及桥—串联系统的可靠性，在这三种新模型下得出了便于操作的Bayes可靠性分析方法和步骤，以及准确的结果。尤其是在这三种模型中还独创性地研究了由相依(即不独立)单元组成的系统的可靠性，并首次将最大熵方法引入含桥联系统模型中，从而将单元可靠性信息综合为系统验前分布，最后就有无系统级信息这两种情况，分别进行讨论，得到了相应的统计分析方法。 第二部分本文首先在样本总体服从均匀分布，参数θ的先验分布是pareto分布的条件下，求得参数的Bayes估计，并在取一种新的损失函数的条件下，得出了平方损失函数的Bayes估计。通过分析，本文给出了平方损失函数的Bayes估计是保守估计的判断标准，以及风险函数的Bayes估计是保守估计的判断标准，并分别给予了证明。接着，作者给出了参数在加权平方损失函数下的Bayes估计和风险函数的Bayes估计。最后本文从矩估计、极大似然估计等角度研究了共轭先验分布Gamma的超参数，给出了几种确定超参数的方法。更多还原

【Abstract】 This paper contains two parts.In the first part, the Bayesian reliablity of complex systems is discussed. On the basis of our analysis to the existing research on the complex system, the related analysis methods are optimized in this paper, resulting one effective new method that the maximum entropy principle is used to analysing the systems with components are dependent each other. In this paper, the following systems are studied: the series system, the bridge system, the series-bridge system and the bridge-series system.Moreover, the above systems are discussed from the two sides: one is that the components are dependent each other; especially the other is that the components are independent each other.In the second part, the super-parametre of conjugate prior distribution Gamma is discussed from the view of maximum likelihood estimation and torque estimatation.This paper shows the method of getting its Bayesian estimation when the samples submit to homogeneous distribution and the prior distribution of parameter 6 is Pareto distribution. This paper gives the yardstick of verdicting risk function that is conservative estimation or not. At the same time, this paper gives the yardstick of verdicting the Bayesian estimation of quadratic loss function that is conservative estimation or not. In the end, The Bayesian estimation of the parameter when it is in the complexion of weighted quadratic loss function is given in this paper.更多还原