Economical Second-Order Designs Based on Irregular Fractions of the 3 n Factorial

There are presented some new economical, nonorthogonal, second-order designs based on irregular fractions of partially balanced type of the 3 n factorial for any number of factors n ≥ 3. The designs generalize those of Rechtschaffner [10]. The complete estimation, variance-covariance, trace, and determinant structures have been derived as explicit functions of n and these quantities compared for the best saturated versus the best augmented design. The efficiencies of the parameter estimates relative to those in other designs of comparable size have been computed.