Keywords: D-optimal design, Response Surface design, Partially Balanced array, Asymmetrical Balanced array, Irregular Fractional Factorial design

Abstract: Three level factorial designs will be discussed that are suitable for small second order designs. The best choice of potential design points will be discussed under the criterion of minimizing the generalized variance of the parameters in the model. Two methods will be illustrated that yield designs with different resolution for the main effects and two factor interactions. Both methods involve the use of Partially Balanced Arrays. The Extended Partially Balanced Array will be defined as a generalization of the Partially Balanced array.