Lee偏差在试验设计中的应用研究

项目名称： Lee偏差在试验设计中的应用研究

项目编号： No.11301546

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 邹娜

作者单位： 中南财经政法大学

项目金额： 22万元

中文摘要： 均匀设计是一种空间填充设计，其理论研究的重点在于寻找合适的均匀性测度，并验证均匀性准则的统计合理性。与已有的偏差相比，Lee偏差能更合理的体现不同水平间的差异，适用于度量高水平设计的均匀性。本项目主要研究基于Lee偏差的均匀性理论，这些结论进一步丰富了均匀设计理论的内容。 （1）基于Lee偏差定义新的均匀性模式，提出相应的最小低阶投影均匀性准则，建立均匀性模式与广义字长型、各阶矩之间的解析关系，验证这一新准则的统计合理性。 （2）构建double设计的Lee偏差与广义字长型间的解析关系，讨论double方法对于设计的均匀性是否具有稳健性。 （3）在Lee距离的基础上定义新的矩，建立最小矩混杂准则与广义最小低阶混杂准则、均匀性准则之间联系，给这一新准则以统计意义上的支撑。 （4）考察均匀性模式与设计效率准则间的联系，从模型稳健性的角度验证最小低阶投影均匀性准则的统计合理性。

中文关键词： 试验设计；均匀设计；Lee偏差；最小低阶Lee矩混杂；Double方法

英文摘要： The uniform experimental design is one kind of space filling designs that can be used for computer experiments and also for industrial experiments when the underlying model is unknown. The measure of uniformity plays a key role in the construction of uniform designs. Recently, based on Lee distance, a so-called Lee discrepancy has been used to explore the pontential application to experiment designs. The Lee discrepancy can expand relationships between the discrete discrepancy and some criteria for factorial designs with multiple levels. The project aims to study the theory of uniformity on Lee dicrepancy. (1)Based on Lee discrepancy, we will propose a new uniformity pattern and the corresponding minimum projection uniformity(MPU) criterion. Our results give some analytic linkages among the uniformity pattern, the generalized wordlength pattern and the power moment, and shall provide a significant statistical justification of Lee discrepancy. (2)We derive results connecting the Lee discrepancy of the double design and the generalized wordlength pattern of the original design, which show the relationship between the uniformity of the double design and that of the original one. (3)Note that the power moment is also based on Hamming distance, which is can only distinguish two values to be equal or not and does not

英文关键词： Experiment of design；Uniform design；Lee discrepancy；Minimum Lee-moment aberration；Double method