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 M k 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 M k , i.e., the full estimation capacity. actional factorial plans in D with the full estimation capacity for k ⩾ 2 are able to discriminate between models in M u 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 2 m 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 M k are also given. Our designs D 4.1 and D 10 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 D 4.2 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 D 4.2 with respect to the criterion functions AD and GD. Our design D 14 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 .