Some characterizations of affinely full-dimensional factorial designs

TL;DR

This paper introduces a new class of two-level fractional factorial designs called affinely full-dimensional designs, which ensure parameter identifiability and optimality properties, especially for certain run sizes.

Contribution

The paper defines affinely full-dimensional factorial designs, analyzes their indicator functions, and demonstrates their optimality for specific run sizes in fractional factorial experiments.

Findings

Design points are not contained in any affine hyperplane over _2.

Parameters of the main effect model are simultaneously identifiable.

For run sizes r b7 5,6,7 (mod 8), the D-optimal design is from this class.

Abstract

A new class of two-level non-regular fractional factorial designs is defined. We call this class an {\it affinely full-dimensional factorial design}, meaning that design points in the design of this class are not contained in any affine hyperplane in the vector space over $\mathbb{F}_2$. The property of the indicator function for this class is also clarified. A fractional factorial design in this class has a desirable property that parameters of the main effect model are simultaneously identifiable. We investigate the property of this class from the viewpoint of $D$-optimality. In particular, for the saturated designs, the $D$-optimal design is chosen from this class for the run sizes $r \equiv 5,6,7$ (mod 8).