混料对称设计最优性的图检验法

李光辉,朱志彬,燕飞,张崇岐

系统科学与数学 ›› 2020, Vol. 40 ›› Issue (2) : 355-365.

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系统科学与数学 ›› 2020, Vol. 40 ›› Issue (2) : 355-365. DOI: 10.12341/jssms13822
论文

混料对称设计最优性的图检验法

    李光辉1,朱志彬2,燕飞3,张崇岐4
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Graphical Method in Testing the Optimality of Symmetrical Mixture Design

    LI Guanghui1, ZHU Zhibin2 ,YAN Fei3 ,ZHANG Chongqi4
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摘要

在混料试验中, 当混料模型较为复杂且混料成份较多时, 要 验证一个设计ξ的最优性是比较困难的. 一方面, 当模型或约束较为复杂时难以证明方差函数是否满足最优性准 则条件, 另一方面, 当混料成份多于3时不能通过绘制方差函数的曲面图来观 察最优性.文章提出一种可用于验证混料对称设计的最优性的图检验法 , 通过 实例分析, 这种方法是有效的.

Abstract

In a mixture experiment, a complex mixture model or a big number of mixture components makes verifying the optimality of the design difficult, i.e., when the model or constraints are complex, it is difficult to prove whether the variance decision function satisfies the optimality criterion, or when the number of mixture components is greater than 3, the optimality cannot be observed by the surface graph of variance decision function. In this paper, a graph checking method is proposed to verify the optimality of symmetrical design of mixture. The effectiveness of this method can be showed by case analysis.

关键词

格子点集 / 对称设计 / 方差函数.

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李光辉 , 朱志彬 , 燕飞 , 张崇岐. 混料对称设计最优性的图检验法. 系统科学与数学, 2020, 40(2): 355-365. https://doi.org/10.12341/jssms13822
LI Guanghui , ZHU Zhibin , YAN Fei , ZHANG Chongqi. Graphical Method in Testing the Optimality of Symmetrical Mixture Design. Journal of Systems Science and Mathematical Sciences, 2020, 40(2): 355-365 https://doi.org/10.12341/jssms13822
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