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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2016, Vol. 33 ›› Issue (1): 36-44.doi: 10.3969/j.issn.1005-3085.2016.01.004

• • 上一篇    下一篇

幻方在趋势无关设计中的研究

马海南1,  陈雪平2,3   

  1. 1- 浙江工业职业技术学院人文社科部，绍兴  312000
    2- 江苏理工学院数理学院，常州 213001
    3- 东南大学数学系，南京 211189
  • 收稿日期:2014-10-08 接受日期:2015-04-09 出版日期:2016-02-15 发布日期:2016-04-15
  • 基金资助:
    国家自然科学基金 (11301073; 11401094)；教育部人文社科基金 (13YJC910006).

Research on Magic Squares in Trend Free Plans

MA Hai-nan1,  CHEN Xue-ping2,3   

  1. 1- Department of Humanities and Social Sciences, Zhejiang Industry Polytechnic College, Shaoxing 312000
    2- School of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001
    3- Department of Mathematics, Southeast University, Nanjing 211189
  • Received:2014-10-08 Accepted:2015-04-09 Online:2016-02-15 Published:2016-04-15
  • Supported by:
    The National Natural Science Foundation of China (11301073; 11401094); the Science Foundation of Ministry of Education of China (13YJC910006).

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摘要： 试验设计中往往会碰到带有趋势干扰因子的情形，这类趋势可以是由时间效应或空间效应引起的．本文探讨了幻方及纯幻方在带有趋势干扰效应设计中的若干应用．首先，利用幻方的组合性质，得到了一类设计因子与趋势干扰因子在参数估计上不混杂的设计；其次，采用纯幻方，进一步得到了多因子试验设计中的趋势无关设计；最后，给出了利用幻方和纯幻方构造相应趋势无关设计的基本方法，同时证明了运用同心幻方进行交叉验证的结果．

关键词: 同心幻方, 多水平, 多项式模型, 多因子试验, 混杂

Abstract:

There are always trend disturbances in design of experiment, which arise from the time trend or the space trend. In this paper, several applications of magic squares and perfect magic squares in trend free plans are discussed. Firstly, based on the combinational properties of magic squares, a class of plans which keep the estimations of design factors and trend disturbance factors independent are obtained. Moreover, by using perfect magic squares, the trend free plans with more factors are provided. Finally, some construction methods of such trend free plans are developed by magic squares and perfect magic squares. Meanwhile, the results between concentric magic squares and cross validation are also proved.

Key words: concentric magic squares, multilevel, polynomial model, multi-factor experiment, alias

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