# Full Factorial

Evaluates all possible combinations of input variable levels. This will resolve all the effects and interactions.

Table 1. . Full Factorial run matrix for a three variable problem (variables A and B have two levels and variable C has three levels).
Run Number A B C
1 1 1 1
2 1 1 2
3 1 1 3
4 1 2 1
5 1 2 2
6 1 2 3
7 2 1 1
8 2 1 2
9 2 1 3
10 2 2 1
11 2 2 2
12 2 2 3

## Usability Characteristics

• For a case with k input variables, each at L levels, a Full Factorial design has L^k runs. For studies with a large number of input variables and levels, the total number of runs is larger. For example, for a study with eight factors and each with three levels, 6561 runs are needed (3^8 = 6561).
• This method may be practical for studies where there is a small number of variables and each variable has two levels, such as yes or no; -1 or 1. This method is not practical for most CAE applications where there are many factors possibly at several levels, and the simulations are costly.
• If the number of levels is not equal across variables, then the total number of runs is calculated by the product of the L^k terms. For example, consider eight variables: five variables with two levels, two variables with three levels and one variable with four levels. The number of full factorial runs is 1152 = 2^5 * 3^2 * 4^1.
• Any data in the inclusion matrix is combined with the run data for post-processing. Any run matrix point which is already part of the inclusion data will not be rerun.
• When the number of levels is less than the defined number of states of a discrete or categorical variable, the assigned levels are based on an equally spaced sample of the ordinal indices.

## Settings

In the Specifications step, Settings tab, change method settings.
Parameter Default Range Description
Number of Runs ${2}^{nd{v}_{2}}{3}^{nd{v}_{3}}...$ 2-1,000,000 Number of new designs to be evaluated. $nd{v}_{i}$ is the number of input variables with i levels. This number is determined automatically based on the number of input variables and levels.
Use Inclusion Matrix Off Off or On Concatenation without duplication between the inclusion and the generated run matrix.