# Orthogonal Array

The Orthogonal Arrays constructed with a fraction of a Full factorial array but the orthogonality (in-dependency) 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. These arrays are often used in an DOE test setup. 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 instead of 3 different factors can be investigated with 8 tests.
 Full Factorial Orthogonal A B C A B C D E F G 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 A B C A B C 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

## Selecting a Orthogonal array

Menu => DOE => Factorial Array
Select the array.

## Combining columns and editing arrays

See edit factorial array.

## Notation of a Orthogonal Array

L = Latin square
a = Amount of tests (rows)
b = Amount of Levels
c = number of columns

 Name Factors 2 Levels 3 Levels 5 Levels L4 3 3 L8 7 7 L9 4 4 L12 11 11 L16 15 15 L18 8 1 7 L25 6 6 L27 13 13 L32 31 31 L36 23 11 12 L50 12 1 11 L54 26 1 25
When 4 or more levels are needed columns can be combined to achieve this (see edit factorial array) .

## L4

=> 3 Factors on 2 levels
 Tests ↓ Factors A B C 1 -1 -1 -1 2 -1 1 1 3 1 -1 1 4 1 1 -1

## L8

=> 7 Factors on 2 levels
 Tests ↓ Factors A B C D E F G 1 -1 -1 -1 -1 -1 -1 -1 2 -1 -1 -1 1 1 1 1 3 -1 1 1 -1 -1 1 1 4 -1 1 1 1 1 -1 -1 5 1 -1 1 -1 1 -1 1 6 1 -1 1 1 -1 1 -1 7 1 1 -1 -1 1 1 -1 8 1 1 -1 1 -1 -1 1

## L9

=> 4 Factors on 3 levels
 Tests ↓ Factors A B C D 1 -1 -1 -1 -1 2 -1 0 0 0 3 -1 1 1 1 4 0 -1 0 1 5 0 0 1 -1 6 0 1 -1 0 7 1 -1 1 0 8 1 0 -1 1 9 1 1 0 -1

## L12

=> 11 Factors on 2 levels
 Tests ↓ Factors A B C D E F G H I J K 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 2 -1 -1 -1 -1 -1 1 1 1 1 1 1 3 -1 -1 1 1 1 -1 -1 -1 1 1 1 4 -1 1 -1 1 1 -1 1 1 -1 -1 1 5 -1 1 1 -1 1 1 -1 1 -1 1 -1 6 -1 1 1 1 -1 1 1 -1 1 -1 -1 7 1 -1 1 1 -1 -1 1 1 -1 1 -1 8 1 -1 1 -1 1 1 1 -1 -1 -1 1 9 1 -1 -1 1 1 1 -1 1 1 -1 -1 10 1 1 1 -1 -1 -1 -1 1 1 -1 1 11 1 1 -1 1 -1 1 -1 -1 -1 1 1 12 1 1 -1 -1 1 -1 1 -1 1 1 -1

## L16

=> 15 Factors on 2 levels
 Tests ↓ Factors A B C D E F G H I J K L M N O 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 2 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 3 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 4 -1 -1 -1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 5 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 6 -1 1 1 -1 -1 1 1 1 1 -1 -1 1 1 -1 -1 7 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 8 -1 1 1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 9 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 10 1 -1 1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1 11 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 12 1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 13 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 14 1 1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 15 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 16 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1

## L18

=> 1 Factor on 2 levels and 7 on 3 levels
 Tests ↓ Factors A B C D E F G H 1 -1 -1 -1 -1 -1 -1 -1 -1 2 -1 -1 0 0 0 0 0 0 3 -1 -1 1 1 1 1 1 1 4 -1 0 -1 -1 0 0 1 1 5 -1 0 0 0 1 1 -1 -1 6 -1 0 1 1 -1 -1 0 0 7 -1 1 -1 0 -1 1 0 1 8 -1 1 0 1 0 -1 1 -1 9 -1 1 1 -1 1 0 -1 0 1-1 0 -1 -1 1 1 0 0 -1 11 0 -1 0 -1 -1 1 1 0 12 0 -1 1 0 0 -1 -1 1 13 0 0 -1 0 1 -1 1 0 14 0 0 0 1 -1 0 -1 1 15 0 0 1 -1 0 1 0 -1 16 0 1 -1 1 0 1 -1 0 17 0 1 0 -1 1 -1 0 1 18 0 1 1 0 -1 0 1 -1

## L25

=> 6 Factors on 5 Levels
 Test ↓ Factors A B C D E F 1 -2 -2 -2 -2 -2 -2 2 -2 -1 -1 -1 -1 -1 3 -2 0 0 0 0 0 4 -2 1 1 1 1 1 5 -2 2 2 2 2 2 6 -1 -2 -1 0 1 2 7 -1 -1 0 1 2 -2 8 -1 0 1 2 -2 -1 9 -1 1 2 -2 -1 0 10 -1 2 -2 -1 0 1 11 0 -2 0 2 -1 1 12 0 -1 1 -2 0 2 13 0 0 2 -1 1 -2 14 0 1 -2 0 2 -1 15 0 2 -1 1 -2 0 16 1 -2 1 -1 2 0 17 1 -1 2 0 -2 1 18 1 0 -2 1 -1 2 19 1 1 -1 2 0 -2 20 1 2 0 -2 1 -1 21 2 -2 2 1 0 -1 22 2 -1 -2 2 1 0 23 2 0 -1 -2 2 1 24 2 1 0 -1 -2 2 25 2 2 1 0 -1 -2

## L27

=> 13 Factors on 3 Levels
 Tests ↓ Factors A B C D E F G H I J K L M 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 2 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 3 -1 -1 -1 -1 1 1 1 1 1 1 1 1 1 4 -1 0 0 0 -1 -1 -1 0 0 0 1 1 1 5 -1 0 0 0 0 0 0 1 1 1 -1 -1 -1 6 -1 0 0 0 1 1 1 -1 -1 -1 0 0 0 7 -1 1 1 1 -1 -1 -1 1 1 1 0 0 0 8 -1 1 1 1 0 0 0 -1 -1 -1 1 1 1 9 -1 1 1 1 1 1 1 0 0 0 -1 -1 -1 10 0 -1 0 1 -1 0 1 -1 0 1 -1 0 1 11 0 -1 0 1 0 1 -1 0 1 -1 0 1 -1 12 0 -1 0 1 1 -1 0 1 -1 0 1 -1 0 13 0 0 1 -1 -1 0 1 0 1 -1 1 -1 0 14 0 0 1 -1 0 1 -1 1 -1 0 -1 0 1 15 0 0 1 -1 1 -1 0 -1 0 1 0 1 -1 16 0 1 -1 0 -1 0 1 1 -1 0 0 1 -1 17 0 1 -1 0 0 1 -1 -1 0 1 1 -1 0 18 0 1 -1 0 1 -1 0 0 1 -1 -1 0 1 19 1 -1 1 0 -1 1 0 -1 1 0 -1 1 0 20 1 -1 1 0 0 -1 1 0 -1 1 0 -1 1 21 1 -1 1 0 1 0 -1 1 0 -1 1 0 -1 22 1 0 -1 1 -1 1 0 0 -1 1 1 0 -1 23 1 0 -1 1 0 -1 1 1 0 -1 -1 1 0 24 1 0 -1 1 1 0 -1 -1 1 0 0 -1 1 25 1 1 0 -1 -1 1 0 1 0 -1 0 -1 1 26 1 1 0 -1 0 -1 1 -1 1 0 1 0 -1 27 1 1 0 -1 1 0 -1 0 -1 1 -1 1 0

## L36

=> 11 Factors on 2 levels and 12 Factors on 3 levels
 Tests ↓ Factors A B C D E F G H I J K L M N O P Q R S T U V W 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 2 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 1 1 1 1 4 -1 -1 -1 -1 -1 0 0 0 0 0 0 -1 -1 -1 -1 0 0 0 0 1 1 1 1 5 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 -1 -1 -1 -1 6 -1 -1 -1 -1 -1 0 0 0 0 0 0 1 1 1 1 -1 -1 -1 -1 0 0 0 0 7 -1 -1 0 0 0 -1 -1 -1 0 0 0 -1 -1 0 1 -1 0 1 1 -1 0 0 1 8 -1 -1 0 0 0 -1 -1 -1 0 0 0 0 0 1 -1 0 1 -1 -1 0 1 1 -1 9 -1 -1 0 0 0 -1 -1 -1 0 0 0 1 1 -1 0 1 -1 0 0 1 -1 -1 0 10 -1 0 -1 0 0 -1 0 0 -1 -1 0 -1 -1 1 0 -1 1 0 1 0 -1 1 0 11 -1 0 -1 0 0 -1 0 0 -1 -1 0 0 0 -1 1 0 -1 1 -1 1 0 -1 1 12 -1 0 -1 0 0 -1 0 0 -1 -1 0 1 1 0 -1 1 0 -1 0 -1 1 0 -1 13 -1 0 0 -1 0 0 -1 0 -1 0 -1 -1 0 1 -1 1 0 -1 1 1 0 -1 0 14 -1 0 0 -1 0 0 -1 0 -1 0 -1 0 1 -1 0 -1 1 0 -1 -1 1 0 1 15 -1 0 0 -1 0 0 -1 0 -1 0 -1 1 -1 0 1 0 -1 1 0 0 -1 1 -1 16 -1 0 0 0 -1 0 0 -1 0 -1 -1 -1 0 1 0 -1 -1 1 0 1 1 0 -1 17 -1 0 0 0 -1 0 0 -1 0 -1 -1 0 1 -1 1 0 0 -1 1 -1 -1 1 0 18 -1 0 0 0 -1 0 0 -1 0 -1 -1 1 -1 0 -1 1 1 0 -1 0 0 -1 1 19 0 -1 0 0 -1 -1 0 0 -1 0 -1 -1 0 -1 1 1 1 -1 0 0 -1 0 1 20 0 -1 0 0 -1 -1 0 0 -1 0 -1 0 1 0 -1 -1 -1 0 1 1 0 1 -1 21 0 -1 0 0 -1 -1 0 0 -1 0 -1 1 -1 1 0 0 0 1 -1 -1 1 -1 0 22 0 -1 0 -1 0 0 0 -1 -1 -1 0 -1 0 0 1 1 -1 0 -1 -1 1 1 0 23 0 -1 0 -1 0 0 0 -1 -1 -1 0 0 1 1 -1 -1 0 1 0 0 -1 -1 1 24 0 -1 0 -1 0 0 0 -1 -1 -1 0 1 -1 -1 0 0 1 -1 1 1 0 0 -1 25 0 -1 -1 0 0 0 -1 0 0 -1 -1 -1 1 0 -1 0 1 1 -1 1 -1 0 0 26 0 -1 -1 0 0 0 -1 0 0 -1 -1 0 -1 1 0 1 -1 -1 0 -1 0 1 1 27 0 -1 -1 0 0 0 -1 0 0 -1 -1 1 0 -1 1 -1 0 0 1 0 1 -1 -1 28 0 0 0 -1 -1 -1 -1 0 0 -1 0 -1 1 0 0 0 -1 -1 1 0 1 -1 1 29 0 0 0 -1 -1 -1 -1 0 0 -1 0 0 -1 1 1 1 0 0 -1 1 -1 0 -1 30 0 0 0 -1 -1 -1 -1 0 0 -1 0 1 0 -1 -1 -1 1 1 0 -1 0 1 0 31 0 0 -1 0 -1 0 -1 -1 -1 0 0 -1 1 1 1 0 1 0 0 -1 0 -1 -1 32 0 0 -1 0 -1 0 -1 -1 -1 0 0 0 -1 -1 -1 1 -1 1 1 0 1 0 0 33 0 0 -1 0 -1 0 -1 -1 -1 0 0 1 0 0 0 -1 0 -1 -1 1 -1 1 1 34 0 0 -1 -1 0 -1 0 -1 0 0 -1 -1 1 -1 0 1 0 1 -1 0 0 1 -1 35 0 0 -1 -1 0 -1 0 -1 0 0 -1 0 -1 0 1 -1 1 -1 0 1 1 -1 0 36 0 0 -1 -1 0 -1 0 -1 0 0 -1 1 0 1 -1 0 -1 0 1 -1 -1 0 1