ABSTRACT
Fractional factorial designs exhibit a property called projection. This means that the subset of significant factors becomes equivalent to a full-factorial design. The full-factorial approach to experimentation covers all combinations of factors, providing valuable information on interactions. Statisticians consider a design to be resolution III, the lowest possible for standard fractional two-level factorials. For a resolution III design hold up three fingers. In this design, at least one main effect is aliased with at least 1 two-factor interaction. The standard two-level designs provide the choice of 4, 8, 16, 32, or more runs, but only for powers of 2. In 1946, Robin Plackett and J. P. Burman invented alternative two-level designs that are multiples of 4. The industrial experimenters have seen several options for the standard two-level design, which apply fractions that are negative powers of 2.
