Follow-up experiments for two-level fractional factorial designs via double semifoldover

The addition of another fraction to an initial experiment is often necessary to resolve ambiguities involving aliasing of factorial effects. One of the most widely used techniques for the selection of a follow-up experiment is foldover. However, semifoldover (i.e., adding half of a foldover fraction) frequently permits estimation of as many effects of interest as provided by a foldover. Thus, as an alternative to foldover, this article investigates the construction and theoretical properties of follow-up experiments obtained via the addition of two $n/2$ -run semifoldover fractions. The strategy (termed double semifolding) provides a means of estimating more effects than can be achieved with a foldover design. Through the use of indicator functions, general properties of double semifoldover designs will be developed. Optimal double semifoldover plans, based on several established design criteria, will be discussed and tabulated for practical use.