Abstract

A supersaturated design (SSD) is a factorial design whose run size is not enough for estimating all the main effects. Such designs have received much recent interest because of their potential in factor screening experiments. This paper first shows that the design obtained by the Kronecker sum of a balanced design and a generalized Hadamard matrix (i.e., a matrix with both itself and its transpose being difference matrices) has some nice properties. Based on these findings, some new methods for constructing $E(f_{\mathit{NOD}})$-optimal SSDs via generalized Hadamard matrices are developed. Meanwhile, the non-orthogonality of the proposed designs is well controlled by the source designs. In addition, some generalized Hadamard matrices with nice properties are constructed for obtaining $E(f_{\mathit{NOD}})$-optimal SSDs. The proposed methods are easy to implement and many new SSDs can then be constructed.

摘要

过饱和设计 (SSD) 是一种因子设计，其运行规模不足以估计所有主效应。这种设计最近受到了很多关注，因为它们在因子筛选实验中具有潜力。本文首先表明，由平衡设计和广义Hadamard 矩阵（即其自身及其转置为差分矩阵的矩阵）的Kronecker 和得到的设计具有一些很好的性质。基于这些发现，一些新的构建方法$乙(F_{\mathit{点头}})$- 开发了通过广义 Hadamard 矩阵优化的 SSD。同时，所提出的设计的非正交性由源设计很好地控制。此外，构造了一些具有良好性质的广义Hadamard矩阵以获得$乙(F_{\mathit{点头}})$- 最佳 SSD。所提出的方法很容易实现，然后可以构建许多新的 SSD。