# Factorial Array

This dialogue is for choosing the desired factorial array to generate a DOE test setup. In 3 tabs there are options: For Response Surface Methodology (RSM)

## Full factorial Array

Test matrix with all possible combination of of the levels like a binary array. These can also generated factor with different amount of 2 levels can be generated see the picture below.

### Examples

#### 3 factors 2 levels

 1 2 3 1 1 1 1 2 2 1 1 3 1 2 1 4 2 2 1 5 1 1 2 6 2 1 2 7 1 2 2 8 2 2 2

#### 2 factors 3 levels

 1 2 1 1 1 2 2 1 3 3 1 4 1 2 5 2 2 6 3 2 7 1 3 8 2 3 9 3 3 10 1 1 11 2 1 12 3 1 13 1 2 14 2 2 15 3 2 16 1 3 17 2 3 18 3 3

## Orthogonal Array

The Orthogonal Arrays constructed with a fraction of a Full factorial array but the orthogonality (independency) between the factors is kept. The factors are independent from each other and in balance. Due to this the factors can be evaluated independently of each other. Interactions are not included in the array but the array can be constructed to make it possible (see Interactions).

The use of Fractional arrays can increase the amount of factors with the same amount of tests. In this case 7 in stead of 3 different factors can be investigated with 8 tests.
 Full Factorial Orthogonal 1 2 3 1 2 3 4 5 6 7 1 1 1 1 ==> 1 1 1 1 1 1 1 2 2 1 1 1 1 1 2 2 2 2 3 1 2 1 1 2 2 1 1 2 2 4 2 2 1 1 2 2 2 2 1 1 5 1 1 2 2 1 2 1 2 1 2 6 2 1 2 2 1 2 2 1 2 1 7 1 2 2 2 2 1 1 2 2 1 8 2 2 2 2 2 1 2 1 1 2

The use of Fractional arrays reduces the amount of test in this case 4 in stead of 8.
 Full Factorial Orthogonal 1 2 3 1 2 3 1 1 1 1 ==> 1 1 1 2 2 1 1 1 2 2 3 1 2 1 2 1 2 4 2 2 1 2 2 1 5 1 1 2 6 2 1 2 7 1 2 2 8 2 2 2

#### Combining columns and editing arrays

See edit factorial array.