Menu
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
Links