Abstract

Two-level fractional factorial designs are often used in screening scenarios to identify active factors. This article investigates the block diagonal structure of the information matrix of nonregular two-level designs. This structure is appealing since estimates of parameters belonging to different diagonal submatrices are uncorrelated. As such, the covariance matrix of the least squares estimates is simplified and the number of linear dependencies is reduced. We connect the block diagonal information matrix to the parallel flats design (PFD) literature and gain insights into the structure of what is estimable and/or aliased using the concept of minimal dependent sets. We show how to determine the number of parallel flats for any given design, and how to construct a design with a specified number of parallel flats. The usefulness of our construction method is illustrated by producing designs for estimation of the two-factor interaction model with three or more parallel flats. We also provide a fuller understanding of recently proposed group orthogonal supersaturated designs. Benefits of PFDs for analysis, including bias containment, are also discussed.

摘要

两水平部分因子设计通常用于筛选场景中以识别活跃因子。本文研究了非正则二层设计信息矩阵的块对角结构。这种结构很有吸引力，因为属于不同对角子矩阵的参数估计是不相关的。这样，最小二乘估计的协方差矩阵被简化并且线性相关性的数量被减少。我们将块对角信息矩阵连接到并行平面设计（PFD）文献，并使用最小相关集的概念深入了解可估计和/或别名的结构。我们展示了如何确定任何给定设计的平行平面数量，以及如何构建具有指定数量平行平面的设计。我们的构造方法的实用性通过生成用于估计具有三个或更多平行平面的二因素相互作用模型的设计来说明。我们还对最近提出的群正交过饱和设计提供了更全面的理解。还讨论了 PFD 对分析的好处，包括偏差遏制。