Direct construction of globally D‐optimal designs for factors at two levels and main effects models

Abstract

AbstractIn developing screening experiments for two‐level factors, practitioners typically are familiar with regular fractional factorial designs, which are orthogonal, globally D‐optimal (ie, 100% D‐efficient), and exist if is a power of two. In addition, nonregular D‐optimal orthogonal designs can be generated for almost any a multiple of four, the most notable being the family of Plackett and Burman1 designs. If resource constraints dictate that is not a multiple of four, while an orthogonal design for two‐level factors does not exist, one can still consider a D‐optimal design. Exchange algorithms are available in commercial computer software for creating highly D‐efficient designs. However, as the number of factors increases, computer searches eventually fail to find the globally optimal design for any or require impractical search times. In this article, we compile state‐of‐the‐art direct construction methods from the literature for producing globally D‐optimal designs for virtually any number of two‐level factors as well as any greater than the number of factors. We summarize the known methods as well as areas for continued research, with the intention of catalyzing research in extending these construction methods.