Page 527 - Design for Six Sigma a Roadmap for Product Development

486 Chapter Thirteen

Clearly, A has the largest percentage contribution, followed by BD and G,
AB, and so on.

Example 13.12 Three kinds of fertilizers are applied to soybeans (Park
1996): nitrogen (N), phosphoric acid (P 2 O 5 ), and potash (K 2 O), and the
response of interest is the average yield in kilograms (kg) per plot of soy-
beans. The factors are assigned as follows:

Levels, kg
Factors 1 2 3
A Nitrogen 0.5 1.0 1.5
B Phosphoric acid 0.3 0.6 0.9
C Potash 0.4 0.7 1.0
An L 9 orthogonal array is used in this experiment. The experiment layout
and data are listed as below:

Factors
A B e C
Experiment no. 1 2 3 4 Response (soybean yield)
1 1 1 1 1 8
2 1 2 2 2 12
3 1 3 3 3 9
4 2 1 2 3 11
5 2 2 3 1 12
6 2 3 1 2 15
7 3 1 3 2 21
8 3 2 1 3 18
9 3 3 2 1 20

Again, using
k k T 2
SS
T t
2
N
n N
n
t 1
and
N n T 2
SS T

y
2
ij
i 1 j 1 N
n
3 T 2
SS A (T 2 T 2 T )
2
9
1 A 1 A 2 A 3 9
1
3
2
2
2
[(8 12 9) (11 12 15) (21 18 20) ]
9
1
(8 12 9 11 12 15 21 18 20) 2
9
158