基于正交表的中心组合设计及其预测方差  

Prediction Variance Study of the Orthogonal-Array-Based Central Composite Design

作　　者：陈雪平 严静 庞中淇 王晓迪 CHEN Xue-ping;YAN Jing;PANG Zhong-qi;WANG Xiao-di(School of Mathematics and Physics,Jiangsu University of Technology,Changzhou 213001,China;Department of Applied Mathematics,Xi'an Jiaotong-Liverpool University,Soochow 215123,China;School of Statistics and Mathematics,Central University of Finance and Economics,Beijing 102206,China)

机构地区：[1]江苏理工学院数理学院,江苏常州213001 [2]西交利物浦大学应用数学系,江苏苏州215123 [3]中央财经大学统计与数学学院,北京102206

出　　处：《数理统计与管理》2023年第6期964-972,共9页Journal of Applied Statistics and Management

基　　金：国家自然科学基金项目(11971204,12271270);江苏省自然科学基金(BK20200108);江苏理工学院中吴青年创新人才支持计划。

摘　　要：预测能力是评价设计优劣的一个重要准则,通过方差散布图可以准确获得设计在一定区域内的预测能力。本文首先介绍了最新提出的基于正交表的中心组合设计(OACD)以及基于极小极大准则的改进设计(OACM),然后证明了无论是OACD设计还是OACM设计,均不具备旋转性,即预测方差在球面上无法达到一致。最后本文给出了在不同因子数下,OACD设计和OACM设计在预测方差上的模拟比较。结果表明,对于方差散布图包含的平均预测方差、最大预测方差、最小预测方差三个指标,OACM设计均一致优于OACD设计,其结果可以为实际试验工作者提供最优设计选择上的参考。Prediction ability is an important criterion for evaluating the quality of design.The prediction ability of design in a certain area can be accurately obtained through Variance Dispersion Graph.Firstly,this paper introduces the newly proposed central combinatorial design based on orthogonal array(OACD)and improved design based on minimax criterion(OACM).Secondly,we prove that neither OACD nor OACM has rotation property.That is,the prediction variance cannot be a constant on the given sphere.Finally,this paper gives a comparison on the prediction variance between OACD nor OACM design under different factor numbers.The results show that OACM design is consistently better than OACD under the three indicators of average prediction variance,maximum prediction variance and minimum prediction variance on the given sphere.The results can provide a reference for the actual experimenter in the selection of optimal design.

关 键 词：正交设计 预测方差 VDG图 设计效率 极小极大准则 

分 类 号：O212[理学—概率论与数理统计] O212.6[理学—数学] TP391[自动化与计算机技术—计算机应用技术]