Optimal fractional factorial plans for main effects and specified two-factor interactions: a projective geometric approach

Abstract

Finite projective geometry is used to obtain fractional factorial plans for m-level symmetrical factorial experiments, where m is a prime or a prime power. Under a model that includes the mean, all main effects and a specified set of two-factor interactions, the plans are shown to be universally optimal within the class of all plans involving the same number of runs.

Development of Research in Experimental Design in India

“…This work was inspired by earlier results in Dey & Mukerjee (1999b) on the connection between orthogonality and optimality. Further results in this line were reported by Chatterjee et al (2002) and Dey et al (2005).…”

“…For instance, one may wish to work with a model which includes the general mean, all main effects and a specified set of two‐factor interactions when prior knowledge is available about the absence of all other interactions. Dey & Suen (2002) used finite projective geometric tools to obtain a large number of universally optimal plans for symmetric factorials under models of this kind. This work was inspired by earlier results in Dey & Mukerjee (1999b) on the connection between orthogonality and optimality.…”

Allocating factors to the columns of an orthogonal array when certain interactions are important

“…The problem of estimating main effects and specified 2-factor interactions via a fractional factorial plan has been studied earlier e.g., by Pesotan (1992, 1997), Wu and Chen (1992), Dey and Mukerjee (1999b) and Dey and Suen (2002). However, the problem addressed in this communication is slightly different from the ones considered hitherto in the literature.…”

Two-level Orthogonal and Saturated Designs for Estimating Main Effects and Certain Important Interactions

“…Franklin and Bailey (1977) tackled this problem from an algorithm point of view. The line of research was further investigated by Dey and Suen (2002), Ke and Tang (2003), Das et al (2006), and Wang (2007).…”