Three Quarter Replicates of 2 n Designs

The 2'-' series of fractions of 2' designs require that the number of experimental runs be an integral power of 2, i.e. 4, 8, 16, 32, 64, . runs. This can be an onerous restriction in a situation in which experimentation is expensive. This is particularly true when an adequate prior estimate of the error variance is available. When these fractions are combined in sets of three, we have the 3(2f-P) series giving designs of 6, 12, 24, 48, 96, ... runs which are intermediate in size between the 27-z series. The purpose of this paper is to discuss the construction and analysis of these designs. The details of the mathematical derivations of some of the statements made in the body of the paper are given in the appendix.