Video 6 explains the design resolution in fractional factorial design of experiments.
For the one-half fraction design in Table 7, the number of letters in the generator (or the word or the defining relation) of the design determine the resolution number of the design. For an example, for the one-half fraction design, the design is called a “resolution of three” if a three-letter generator, ABC is used in developing the design. For the one-half fraction design, if a five-letter generator word is used, the design is called a “resolution of five.”
Table 7. One-Half Fraction Design Generator, Resolution, Alias Structures, the resolution
The alias structure for the word ABC is A=BC, B = AC, and C = AB. Therefore, the main effect is aliased with the two-factor interaction in a resolution III design, and no main effects are aliased with any other main effect. The aliased structure for the word ABCD is A = BCD, B = ACD, C = ABD, D = ABD, and AB = CD, AC = BD, and AD = BC. Therefore, the main effects are aliased with the three-factors interactions and the two-factors interactions are aliased with the other two-factors interactions in a resolution IV design. And, no main effects are aliased with any other main effect. Therefore, the general definition for the resolution for any fractional design (e.g., half, quarter, 1/8th, 1/16th, etc.) can be developed as in Table 8. To determine the correct resolution of design, the “must not be aliased with” column must be primarily used. Resolution can be thought of as the screen resolution. Higher resolution will produce better output but cost more. Although the higher resolution of the design has been suggested (Box et al., 2005; Montgomery, 2019), the lower resolution would work just fine for screening variables. As the fractional factorial design is primarily utilized for screening factors/variables, resolution of III will make more sense than any higher resolution design in screening purposes to reduce the total number of initial experiments. Nevertheless, when possible, higher should be preferred over lower resolution without increasing the number of experiments in the screening process.
Table 8. Determine the Design Resolution Rules