带有异常值的应力—强度模型的贝叶斯估计

发布时间：2018-04-14 19:17

本文选题：应力-强度模型 + 瑞利分布　；参考：《吉林大学》2017年硕士论文

【摘要】：应力-强度模型在机械装置或电器元件的可靠性评估中应用广泛,其中,应力定义为引起元件或装置失效的载荷,强度定义为元件或装置在承受外部载荷时能满意地完成规定任务而没有失效的能力,可靠性参数定义为影响失效的应力没有超过控制失效的强度的概率.本文研究的是应力和强度均服从瑞利分布且带有异常值的应力-强度模型的参数估计问题,用数学语言来表述,即研究可靠性参数R=P(YX)的估计问题,其中变量Y和X是相互独立的,变量Y代表应力,服从参数是λ的瑞利分布,变量X代表强度,样本中带有2个异常值,服从参数是θ和β的瑞利分布.在国外学者对带有异常值的应力-强度模型的研究中,对参数R的估计基本以经典估计方法为主,运用贝叶斯估计方法的研究文章相对较少,国内学者对应力-强度模型的研究基本不涉及试验样本带有异常值的情况.在本文中,将运用贝叶斯估计的方法来研究参数R=P(YX)的估计问题,相较于经典方法把未知参数看作是确定的常数,贝叶斯估计把未知参数看作是随机变量,利用样本分布和先验分布的全部信息来进行统计推断.在本文中,参数R的贝叶斯估计将会在平方损失,0-1损失和对称熵损失这三种损失函数下给出,并根据推导得到的结果进行估计值偏差的数值模拟,然后比较这三种损失函数下得到的贝叶斯估计值的估计效果,最后得出结论,运用贝叶斯估计的方法来研究带有异常值的应力-强度模型行之有效.
[Abstract]:The stress-strength model is widely used in the reliability evaluation of mechanical or electrical components, in which the stress is defined as the load that causes the failure of the components or devices.Strength is defined as the ability of components or devices to perform specified tasks satisfactorily without failure under external load. The reliability parameter is defined as the probability that the stress affecting failure does not exceed the strength of control failure.In this paper, we study the parameter estimation of stress-strength model with Rayleigh distribution and outliers, which is expressed by mathematical language, that is, the estimation of reliability parameter RPX.The variables Y and X are independent of each other, the variable Y represents the stress, the subordinate parameter is the Rayleigh distribution of 位, the variable X represents the strength, the sample has two abnormal values, and the subordinate parameter is the Rayleigh distribution of 胃 and 尾.In the research of stress-strength model with outliers abroad, the estimation of parameter R is mainly based on classical estimation method, but there are few articles using Bayesian estimation method.The research on the stress-strength model by domestic scholars basically does not involve the case where the test sample has outliers.In this paper, the Bayesian estimation method is used to study the parameter estimation problem. Compared with the classical method, the unknown parameter is regarded as a definite constant, and the unknown parameter is regarded as a random variable in Bayesian estimation.All the information of sample distribution and prior distribution are used for statistical inference.In this paper, the Bayesian estimation of parameter R will be given under the three loss functions of squared loss 0-1 loss and symmetric entropy loss.The results of Bayesian estimation under these three loss functions are compared, and the conclusion is drawn that it is effective to use Bayesian estimation to study the stress-strength model with outliers.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.8

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