Projection properties of no-confounding designs for six, seven and eight factors in 16 runs

Abstract

The no-confounding (NC) designs introduced by Jones and Montgomery (2010) are 16-run fractional factorials for six to eight factors having partial aliasing of the main effects by a few two-factor interactions but avoiding any complete confounding of any main effects or two-factor interactions with each other. These designs potentially allow for unambiguous identification and parameter estimation of all main effects and a couple of active two-factor interactions without additional runs. These designs provide an alternative to the well-known 16 run regular fractional factorial designs in six, seven and eight factors. The main drawback of the regular fractional factorial designs is that all two factor interactions are completely aliased with one another, which makes identification of two-factor interactions possible only with the deployment of additional runs. While the projection properties of the minimum aberration regular fractional factorial designs are well understood, the projection properties of the NC designs have not been studied. We present the projection properties of the NC designs for six, seven and eight factors in 16 runs. These projection properties are then used to suggest analysis strategies for these designs given that the principle of effect sparsity holds.