New families of Q_B-optimal saturated two-level main effects screening designs

Abstract

Abstract:In this paper, we study saturated two-level main effects designs which are commonly used for screening experiments. The QB criterion, which incorporates experimenters' prior beliefs about the probability of factors being active is used to compare designs. We show that under priors with more weight on models of small size, p-efficient designs should be recommended; when models with more parameters are of interest, A-optimal designs would be better. We identify new classes of saturated main effects designs between these two designs under different priors. The way in which the choice of designs depends on experimenters' prior beliefs is demonstrated for the cases when the number of runs N ≡ 2 mod 4. A novel method of construction of QB-optimal designs using conference matrices is introduced. Complete families of optimal designs are given for N = 6, 10, 14, 18, 26, 30.

Discussion of “21st century screening experiments: What, why, and how”

“…We can move smoothly from the hard criteria to (or towards) A s -optimality by adjusting the priors, which act like hardness parameters, getting many different designs on the way. Tsai and Gilmour (2010) showed this in general and Tsai and Gilmour (2015) studied the case of saturated two-level main-effects designs in more detail. These criteria are even more flexible than this.…”

“…• Tsai et al (2000) also showed how fold-over methods could be used to obtain three-level screening designs, giving the same designs as described in Jones' paper, e.g. the 13-run design in Table 1 appears in Tsai et al (2000).…”

“…We can nest soft criteria inside hard criteria, e.g. search for a Q B -optimal among the class of orthogonal main effects designs, as in Tsai et al (2000Tsai et al ( , 2004 for three-level designs. We can have any number of factors, with any number of levels, in any number of runs, with any maximal (linear) model; blocking can also be allowed for, as will be shown in forthcoming work.…”

“…• Tsai et al (2000) used a columnwise-pairwise algorithm to find orthogonal and nearly-orthogonal three-level main effects designs. The restriction that main effects should be as nearly orthogonally estimated as possible means that each factor should be level-balanced, so that an algorithm which makes use of this restriction is appropriate.…”

“…• Tsai and Gilmour (2015) used conference matrices to construct twolevel saturated main effects designs.…”