Plackett-Burman designs and three quarter fractional factorial designs are both well established in the statistical literature yet have never been combined and studied. Plackett-Burman designs are often non-regular and are thus subject to complex aliasing. However, Plackett-Burman designs have the advantage of run-size efficiency (over the usual 2^(k) factorials) and taking three quarters of a Plackett-Burman design further improves this benefit. By considering projections of these designs, we constructed a catalog of designs of resolution V and ranked by D-efficiency.

When approaching a new research problem, we often use screening designs to determine which factors are worth exploring in more detail. Before exploring a problem, we don't know which factors are important. When examining a large number of factors, it is likely that only a handful are significant and that even fewer two-factor interactions will be significant. If there are important interactions, it is likely that they are connected with the handful of significant main effects. Since we don't know beforehand which factors are significant, we want to choose a design that gives us the highest probability a priori of being able to estimate all significant main effects with their associated two-factor interactions. This project examines the methodology of finding designs that do not rely on an assumed model. We propose a method of modifying the D-Optimality criteria that averages over models with a common set of main effects and varying subsets of two-factor interations. We also calculate the proportion of the subsets that produce estimable designs. We use these results to find the best models for given run size and number of main effects.