加速寿命试验中小样本最优设计方法

项目名称： 加速寿命试验中小样本最优设计方法

项目编号： No.11201345

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 徐安察

作者单位： 温州大学

项目金额： 22万元

中文摘要： 在加速寿命试验中，最优设计一直是最重要的研究内容之一，在工业上有着广泛的应用，但是目前最优设计都是基于大样本近似方法，这在小样本情形下会出现较大的偏差，而对小样本最优设计的研究一直没有相关文献。本课题利用极大似然估计高阶近似和Edgeworth展开在小样本情形下对经典最优设计进行修正；结合回归设计方法提高贝叶斯最优设计中蒙特卡洛法的计算效率，避免了曲线拟合的步骤；从信息论的角度提出新的最优设计准则：先验分布与后验分布的Kullback-Liebler距离的期望最大，并研究该准则与已有准则的关系，给出两种方法计算最优方案。本项目将为小样本情形下的最优设计提供新方法，并从信息论的角度提出研究最优设计的新思路。

中文关键词： 最优设计；小样本；蒙特卡洛；Kullback-Liebler 距离；加速寿命试验

英文摘要： Optimal design is one of the most important contents in the accelerated life tests, which is widely applied in industry. However, all the optimal designs are based on the large sample approximation method, which will have large bias in the case of small sample size. Morever, there are no literatures about small sample optimal design until now. In this project, we utilize the high order approximation of maximum likelihood estimators and Edgeworth expansion to modify the classical optimal design in the case of small sample size, and apply regression design method to improve the efficiency of Monte Carlo method used in Bayesian optimal design, which also avoids the step of curve fitting. Besides, a new optimal design criteria is proposed from the perspective of information theory, that is, maximizing the expectation of the Kullback-Liebler distance between prior distribution and posterior distribution. Then we consider the relationship between the criteria and the given criterias, and give two methods to compute the optimal design. This project will provide some new methods to compute the optimal design when the sample size is small, and present a new way from the information theory perspective to study the optimal design.

英文关键词： Optimal design；small sample size；Monte Carlo；Kullback-Liebler distance；accelerated life test