• Two-Level Full Factorial
 • Two-Level Regular Fractional Factorial
 • Plackett-Burman Designs
 • Mixed-Level Designs
 • Cotter Designs
A regular fractional factorial design also has a sample size that is a power of two. For two-level designs, if k is the number of factors, the number of runs in a regular fractional factorial design is 2k – p where p < k. A 2k – p fractional factorial design is a 2-p fraction of the k-factor full factorial design. Like full factorial designs, regular fractional factorial designs are orthogonal.
A full factorial design for k factors provides estimates of all interaction effects up to degree k. But because experimental runs are typically expensive, smaller designs are preferred. In a smaller design, some of the higher-order effects are confounded with other effects, meaning that the effects cannot be distinguished from each other. Although a linear combination of the confounded effects is estimable, it is not possible to attribute the variation to a specific effect or effects.
 Number of Factors Design Two–Level Three–Level L18 John and L18 Taguchi 1 7 L18 Chakravarty 3 6 L18 Hunter 8 4 L36 Taguchi 11 12
Note: By default, Cotter designs are not included in the Design List. To include Cotter designs, deselect Suppress Cotter Designs in the Screening Design red triangle menu. To always show Cotter designs, select File > Preferences > Platforms > DOE and deselect Suppress Cotter Designs.
For k factors, a Cotter design has 2k + 2 runs. The design structure is similar to the “vary one factor at a time” approach.
 • A run is defined with all factors set to their high level.
 • For each of the next k runs, one factor in turn is set at its low level and the others high.
 • The next run sets all factors at their low level.
 • For each of the next k runs, one factor in turn is set at its high level and the others low.
 • The runs are randomized.
When you construct a Cotter design, the design data table includes a set of columns to use as regressors. The column names are of the form <factor name> Odd and <factor name> Even. They are constructed by summing the odd-order and even-order interaction terms, respectively, that contain the given factor.
For example, suppose that there are three factors, A, B, and C. Cotter Design Table shows how the values in the regressor columns are calculated.
 Effects Summed for Odd and Even Regressor Columns AOdd = A + ABC AEven = AB + AC BOdd = B + ABC BEven = AB + BC COdd = C + ABC CEven = BC + AC

Help created on 9/19/2017