On The Study Of D-Optimal Saturated Designs For Mean, Main Effects and $F_1$-Two-Factor Interactions For $2^k$-Factorial Experiments

TL;DR

This paper develops methods for constructing D-optimal saturated designs in factorial experiments, focusing on mean, main effects, and specific two-factor interactions, with particular strategies for different interaction structures.

Contribution

It introduces new methods for creating D-optimal saturated designs that include mean, main effects, and selected two-factor interactions in $2^k$-factorial experiments.

Findings

Constructed D-optimal saturated designs for full interaction cases.

Discussed design construction for partial interaction scenarios.

Provided specific methods for different interaction structures.

Abstract

The goal of this paper is to develop methods for the construction of saturated designs that include the mean, main effects and the two-factor interactions of one factor with a subset of the remaining factors. If one factor is interacting with all the remaining factors give a method for the construction of a d-optimal saturated design. If one factor is interacting with a proper subset of the remaining factor we discuss the saturated d-optimal design for specific cases.