加倍与投影：一种构造分辨率为iv的两水平设计的方法
Doubling and projection: a method of constructing two-level designs of resolution iv
摘要：
给定一个分辨率为IV的两水平正则部分析因设计，加倍方法产生另一个分辨率为IV的设计，该设计使试验规模和初始设计的因子数都加倍。另一方面，分辨率为IV的设计在因子子集上的投影是分辨率为IV或更高。最近的工作在文献中的射影几何基本上确定了结构的所有定期设计的决议IV与$n\geq N/4+1$方面的加倍和投影，其中$N$是运行大小和$n$是一些因素。这些结果意味着，例如，具有$5N/16<n\leq N/2$的分辨率IV的所有正则设计必须是具有$N/2$因子的分辨率IV的正则设计的投影。我们证明了，对于$9N/32\leq n\leq 5N/16$，所有的最小像差设计都是具有$5N/16$因子的设计的投影，该因子是通过重复加倍由$I=\mathit{ABCDE}$定义的2个$^{5-1}$设计而构造的。为了证明这一结果，我们还得到了一些属性的加倍，包括一个身份的设计字长模式，其双重和结果，做同样的别名模式的两个因素的相互作用。
英文摘要：
Given a two-level regular fractional factorial design of resolution IV, the method of doubling produces another design of resolution IV which doubles both the run size and the number of factors of the initial design. On the other hand, the projection of a design of resolution IV onto a subset of factors is of resolution IV or higher. Recent work in the literature of projective geometry essentially determines the structures of all regular designs of resolution IV with $n\geq N/4+1$ in terms of doubling and projection, where $N$ is the run size and $n$ is the number of factors. These results imply that, for instance, all regular designs of resolution IV with $5N/16<n\leq N/2$ must be projections of the regular design of resolution IV with $N/2$ factors. We show that, for $9N/32\leq n\leq 5N/16$, all minimum aberration designs are projections of the design with $5N/16$ factors which is constructed by repeatedly doubling the 2$^{5-1}$ design defined by $I=\mathit{ABCDE}$. To prove this result, we also derive some properties of doubling, including an identity that relates the wordlength pattern of a design to that of its double and a result that does the same for the alias patterns of two-factor interactions.
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