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Title: Construction of two-level factorial and fractional factorial designs with runs in blocks of size two Authors:  Janet Godolphin - Surrey (United Kingdom) [presenting]
Abstract: In many experiments involving factorial and fractional factorial designs, attention is focused on estimation of all main effects and two factor interactions. Design construction are considered when, due to practical constraints, runs are arranged in blocks of size two. For $p$ factors, and $M$ at least as large as a given function of $p$, a construction approach is provided which generates all designs in which $M$ replicates are arranged in blocks of size two so that all main effects and two factor interactions are estimable. The method incorporates recognition of isomorphic designs to avoid double counting. A design ranking is proposed to give guidance on design selection which prioritises estimation of main effects. This is useful in practice since for some $p$, $M$ combinations the number of designs is large (for example, for $p=8$ and $M=4$ there are 343 designs) and there can be considerable variation in the quality of estimation between designs. The full factorial designs can be used as a source of root designs for construction of designs in fractional replicates, again in blocks of size two. The method is illustrated by examples with up to $p=15$ factors.