Available Two Level Factorial Designs

The available two level factorial designs are shown next. This information is applicable to designs with standard response data, as well as robust parameter designs and reliability DOE.

This table provides information about the available combinations of the number of factors and the number of runs. The two level full factorial designs are displayed in white cells, and the information shown in the cells is (number of levels)^(number of factors), which yields the number of runs.

The two level fractional factorial designs are displayed in green, yellow and red cells, where:

The information shown in the cells is the design in 2k-p form. k represents the number of factors used in the design. The fractionality of the design is equal to 1/2p, or 2-p. Thus, the design is represented by 2k(2-p), or 2k-p. Note that in such designs, the number of generators (i.e., the factorial interactions whose effects will be aliased with the main effects of particular factors) is also equal to p.
- For example, with a 25-3 design, k = 5 and p = 3. Thus, the design has 5 factors, its fractionality is 1/23 (or 1/8), and it uses 3 generators.
Designs in green cells are resolution V or higher. Such designs have a relatively low degree of aliasing (e.g., in resolution V designs, main effects may be aliased with four-factor interactions, and two-factor interactions may be aliased with three-factor interactions). These designs are therefore considered to be quite reliable to use without significant loss of information.
Designs in yellow cells are resolution IV (i.e., main effects may be aliased with three-factor interactions, and two-factor interactions may be aliased with each other). Such designs may be appropriate for screening, as main effects can be free of aliasing with two-factor interactions, but some detailed information is lost.
Designs in red cells are resolution III (i.e., main effects may be aliased with two-factor interactions, and two-factor interactions may be aliased with each other). This can obscure the effects of the factors. If you choose to use such a design, you should be very careful when specifying the generators.

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