Factorial Designs

Factorial designs are typically used for screening factors/interactions. In other words, they help you determine which factors have a significant effect on the response and identify interactions between those factors. The following four types of factorial designs are available:

• Two Level Factorial: Use this design to investigate the main effects and/or interaction effects of a few factors run at two levels each. You can investigate all factors/interactions (full factorial) or only a subset of them (fractional factorial).
• Placket-Burman Factorial: This is a special category of two level fractional factorial design. Use this design to investigate the main effects of multiple factors run at two levels each, using few runs.
• General Full Factorial: Use this design to investigate the main effects and interaction effects of multiple factors run at different numbers of levels (for example, two factors at two levels each and two factors at three levels each).
• Taguchi OA Factorial: Use this design to investigate to investigate the main effects of multiple factors run at different numbers of levels, using few runs. This design can be thought of as a general fractional factorial design.

When selecting a factorial design type, it is important to keep these considerations in mind:

• Full factorial designs test all possible combinations of factors at each level. While such designs yield comprehensive data, they may not be feasible due to constraints on time, money and/or number of samples available for testing.
• Fractional factorial designs test a subset of the possible combinations of factors at the levels in question. This allows for the screening of larger numbers of factors/levels with less investment of time, money and/or samples. However, it also results in some loss of data for analysis, as eliminating runs naturally reduces the ability of the design to fully examine all possible effects.

More specifically, fractionality results in some level of aliasing (or confounding), where the effect of a certain factor or factorial interaction cannot be separated from another effect. Designs in which main effects are aliased with lower-order interactions are said to be low resolution and are appropriate for screening (e.g., a resolution III design, in which main effects may be aliased with second-order interactions, which are interactions of two factors). Fractional factorial designs of higher resolution, along with full factorial designs, may also be useful for studying factorial effects and interactions in depth and/or for optimization. Resolution is presented in more detail in Two Level Factorial Designs.

• Using two levels per factor is generally sufficient for screening experiments. However, to test for curvature (thereby identifying factors and interaction that merit in-depth analysis) either center points or additional levels must be used. If factors have a significant curvature effect on the response, you should investigate their quadratic effects using response surface methodology.

For more information about how to use the design types, please consult the documentation on design folios.