21.4.3.2. Resolution of Experimental Designs

An experimental design is of resolution \(R\) if no \(p-\) factor effect is aliased with another effect containing less than \(R-p\) factors. When the fractional factorial design is developed, the defining relation \(\left( I \right)\) is composed of roman letters. As an example, \({{2}^{3-1}}\) design is constructed with the defining relation \(I=ABC\) or \(I=-ABC\). In this case, the minimum number of letters in the defining relations represents the resolution of design. Hence, \({{2}^{3-1}}\) design is called a resolution III.

  1. Resolution III designs. These are designs in which no main effects are aliased with any other main effect, but main effects aliased with two-factor interactions and two-factor interactions may be aliased with each other. A \({{2}^{3-1}}\) design with \(I=ABC\) is of resolution III \(\left( 2_{III}^{3-1} \right)\). These are main effects only designs.

  2. Resolution IV designs. These are designs in which no main effect is aliased with any other main effect or with any two-factor interaction, but two-factor interactions are aliased with other. A \({{2}^{4-1}}\) design with \(I=ABCD\) is of resolution IV \(\left( 2_{IV}^{4-1} \right)\). These are main effects clear designs.

  3. Resolution V designs. These are designs in which no main effect or two-factor interaction is aliased with any other main effect or two-factor interaction, but two-factor interactions are aliased with three-factor interactions. A \({{2}^{5-1}}\) design with \(I=ABCDE\) is of resolution V \(\left( 2_{V}^{5-1} \right)\). These are two-factor interactions clear designs.