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混料切片试验设计

熊子康1,刘力惟1,宁建辉1,覃红1,2   

  1. 1. 华中师范大学数学与统计学学院, 武汉 430079; 2. 中南财经政法大学统计与数学学院,武汉 430073
  • 出版日期:2020-02-25 发布日期:2020-05-29

熊子康,刘力惟,宁建辉,覃红. 混料切片试验设计[J]. 系统科学与数学, 2020, 40(2): 262-274.

XIONG Zikang, LIU Liwei, NING Jianhui,QIN Hong. Sliced Design for Experiments with Mixtures[J]. Journal of Systems Science and Mathematical Sciences, 2020, 40(2): 262-274.

Sliced Design for Experiments with Mixtures

XIONG Zikang1 ,LIU Liwei1 ,NING Jianhui1 ,QIN Hong 1,2   

  1. 1. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079; 2. Zhongnan University of Economics and Law, Wuhan 430073
  • Online:2020-02-25 Published:2020-05-29

混料试验设计在众多领域中都有广泛的应用, 有时试 验者不仅仅需要考虑各混料成分所占比例对响应变量的影响, 同时 还关心其它被称为过程变量的因素. 在实际中, 对于这类问题通常 使用的设计方案是混料设计和因子设计的组合设计. 这种组合设计在 过程变量的不同水平组合下, 使用的是相同的设计阵, 因此空间填充 性较差. 基于混料球体堆积设计, 文章提出了一类新的混料设计, 称之为混料切片设计, 它的整体设计和所有子设计(过程变量的每一水平组合对应的混料设计)都具有很好的空间填充性, 从而比组合设计有更好的模型稳健性. 基于同余子群的陪集分解方法, 针对过程变量水平组合数的不同情况提出了相应的简单快速的构造算法, 文章最后的数值例子解释了算法的可行性和设计的有效性.

Design for experiment with mixtures are widely used in many fields, sometimes experimenters not only consider the influence of components in mixtures on response variable, but also care about other factors known as process variables at the same time. In practice, for this kind of problem the commonly used design is the combinatorial design of mixture design and factorial design. This kind of design considers the same mixture design for different level combinations of process variables so that its space filling property is poor. In this paper, based on sphere packing design for experiments with mixtures, sliced designs for experiments with mixtures are further put forward. Their full design and all subdesigns (points with mixture variables corresponding to each level-combination of process variables) all have good space-filling property, which makes it have better model robustness than traditional combinatorial designs. For different situations about the number of slices, simple and fast algorithms are proposed based on coset decomposition with congruence subgroups. Finally, some numerical examples explain the feasibility of algorithms and the effectiveness of designs proposed in this paper.

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