均匀部因子设计
Uniform fractional factorial designs
摘要：
最小像差准则在具有名义因子的部分析因设计的选择中经常被使用。然而，对于具有定量因子的设计，因子的水平置换可能改变其几何结构和统计特性。本文除用最小象差准则外，还用均匀性进一步判别部分析因设计。我们发现，最小像差设计平均有低的差异。本文提出了一种构造均匀最小象差设计的有效方法，并得到了具有27和81次试验的最优设计。这些设计具有良好的一致性，是研究定量因素的有效方法。
英文摘要：
The minimum aberration criterion has been frequently used in the selection of fractional factorial designs with nominal factors. For designs with quantitative factors, however, level permutation of factors could alter their geometrical structures and statistical properties. In this paper uniformity is used to further distinguish fractional factorial designs, besides the minimum aberration criterion. We show that minimum aberration designs have low discrepancies on average. An efficient method for constructing uniform minimum aberration designs is proposed and optimal designs with 27 and 81 runs are obtained for practical use. These designs have good uniformity and are effective for studying quantitative factors.
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