Augmenting 2 n −1 Designs

After a 2 n−k fractional factorial has been analysed, an experimenter may wish to carry out a further fraction to improve some estimates and break chains of aliases. The problem of augmenting a 2 n−1 half replicate by a nonoverlapping 2 n−k design is discussed. In each alias set for the 2 n−k fraction the effects occur in pairs as aliases from the half replicate. If only one of these pairs in a given alias set contains two nonnegligible effects, then that chain is broken. If more than one pair has both effects nonnegligible, no chains are broken. Procedures are given for augmenting four-letter plans for four or six factors.