In the Screening Design platform, the design list for factorial designs includes the design resolution. The resolution of a design is a measure of the degree of confounding in the design. The trade-off in screening designs is between the number of runs and the resolution of the design. A factorial screening design of resolution R contains the complete factorial design for any subset of R-1 factors. Resolution III, IV, and V designs are of greatest interest and are defined as follows.
Resolution III
Designs in which no main effects are confounded with any other main effect.
Resolution IV
Designs in which no main effects are confounded with any other main effect or any two-factor interaction.
Resolution V
Designs in which no main effect or two-factor interaction is confounded with any other main effect or two-factor interaction. However, two-factor interactions are confounded with three-factor interactions.
The designs in the Screening Design List include a resolution number and a brief description of the effects that are estimable when using that design. The resolutions are 3, 4, 5, 5+, and >6:
3 - Main Effects Only
A resolution III design in which only main effects are estimable.
4 - Some 2-factor interactions
A resolution IV design in which main effects and some two-factor interactions are estimable. The two-factor interactions are confounded.
5 - All 2-factor interactions
A resolution V design in which main effects and all two-factor interactions are estimable. Three-factor interactions are confounded with the two-factor interactions.
5+ - All 2-factor interactions
A resolution V design in which main effects and all two-factor interactions are estimable. Some higher order interactions are estimable while others are confounded. The design is not a full factorial design.
>6 - Full Resolution
A full factorial design. There is no confounding of effects of any order.
A minimum aberration design is one that minimizes the number of confoundings for a given resolution. A minimum aberration design of a given resolution minimizes the number of words in the defining relation that are of minimum length. For a description of words, see Change Generating Rules. For a discussion of minimum aberration designs, see Fries and Hunter (1984).