三水平逆耶茨序设计的低阶混杂性质
Lower-Order Confounding Properties of Inverse Yates-Order Designs with Three Levels
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摘要: 在三水平正规设计中, 低阶成分效应的混杂信息对选择最优设计至关重要. 本文研究一类三水平逆耶茨序设计D_q(n), 其中q为独立列个数, n为因子个数, 得到设计D_q(n)在三种情况下低阶混杂信息的结果: (i) q<n<3^q-1,n=2k,k\in N; (ii) q<n<3^q-1,n=2k+1,k\in N; (iii) 3^q-1\leq n<(3^q-1)/2, 通过实例来演示上述结果.Abstract: It is important to consider the confounding information of lower-order component effects when choosing the optimal design in three-level regular designs. This paper studies a class of three-level inverse Yates-order designs D_q(n), where q and n are the numbers of independent columns and factors, respectively. The lower-order confounding information of designs D_q(n) are given according to the three cases: (i) q<n<3^q-1,n=2k,k\in N; (ii) q<n<3^q-1,n=2k+1,k\in N; (iii) 3^q-1\leq n<(3^q-1)/2. The above results are illustrated by examples.