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.
Experiments are classified by resolution number into these groups:
• Resolution 3 means that some main effects are confounded with one or more two-factor interactions. In order for the main effects to be meaningful, these interactions must be assumed to be negligible.
• Resolution 4 means that main effects are not confounded with other main effects or two-factor interactions. However, some two-factor interactions are confounded with other two-factor interactions.
• Resolution 5 means that there is no confounding between main effects, between main effects and two-factor interactions, and between pairs of two-factor interactions. Some two-factor interactions are confounded with three-factor interactions.
• Resolution 5+ means that the design has resolution greater than 5 but is not a full factorial design.
• Resolution 6 means that there is no confounding between effects of any order. The design is a full factorial design.
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).