Optimum two level fractional factorial plans for model identification and discrimination

Model identification and discrimination are two major statistical challenges. In this paper we consider a set of models Mk for factorial experiments with the parameters representing the general mean, main effects, and only k out of all two-factor interactions. We consider the class D of all fractional factorial plans with the same number of runs having the ability to identify all the models in Mk, i.e., the full estimation capacity.The fractional factorial plans in D with the full estimation capacity for k⩾2 are able to discriminate between models in Mu for u⩽k*, where k*=(k/2) when k is even, k*=((k-1)/2) when k is odd. We obtain fractional factorial plans in D satisfying the six optimality criterion functions AD, AT, AMCR, GD, GT, and GMCR for 2m factorial experiments when m=4 and 5. Both single stage and multi-stage (hierarchical) designs are given. Some results on estimation capacity of a fractional factorial plan for identifying models in Mk are also given. Our designs D4.1 and D10 stand out in their performances relative to the designs given in Li and Nachtsheim [Model-robust factorial designs, Technometrics 42(4) (2000) 345–352.] for m=4 and 5 with respect to the criterion functions AD, AT, AMCR, GD, GT, and GMCR. Our design D4.2 stands out in its performance relative the Li–Nachtsheim design for m=4 with respect to the four criterion functions AT, AMCR, GT, and GMCR. However, the Li–Nachtsheim design for m=4 stands out in its performance relative to our design D4.2 with respect to the criterion functions AD and GD. Our design D14 does have the full estimation capacity for k=5 but the twelve run Li–Nachtsheim design does not have the full estimation capacity for k=5.