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Design Optimization:Taguchi’s Robust Parameter Design 521

it is very easy (by evaluating the partial derivatives of R T,on versus R 1 , R 2 ,
etc.) to determine whether R T,on increases whenever R 1 decreases, R 2
increases, R 4 decreases, E 0 increases, or R Z decreases and vice versa.
Therefore, R 1 at low level, R 2 at high level, R 4 at low level, E 0 at high level,
and R Z at low level is one extreme combination of noise levels that will place
R T,on on the high side. On the other hand, R 1 at high level, R 2 at low level,
R 4 at high level, E 0 at low level, and R Z at high level is another extreme com-
bination of noise levels that will put R T,on on the low side. In summary, we
can use the following three compounded noise factors:
N1(R 1 ) 1 ,(R 2 ) 3 ,(R 4 ) 1 ,(E 0 ) 3 ,(E Z ) 1
N2(R 1 ) 2 ,(R 2 ) 2 ,(R 4 ) 2 ,(E 0 ) 2 ,(E Z ) 2
N3(R 1 ) 3 ,(R 2 ) 1 ,(R 4 ) 3 ,(E 0 ) 1 ,(E Z ) 3
where (R 1 ) 1 denotes that R 1 is at level 1; (R 2 ) 3 , that R 2 is at level 3; and so
on. By using this set of compounded noise factors, for each run in the inner
array, we will obtain three output response observations under compounded
noise conditions specified by N1, N2, and N3.

14.5 Parameter Design for
Smaller-the-Better Characteristics
For smaller-the-better characteristics, the steps for a Taguchi para-
meter design will be as follows:

1. Select an appropriate output quality characteristic to be optimized.
2. Select control factors and their levels, identifying their possible
interactions.
3. Select noise factors and their levels; if there are many noise factors,
use compound noise factors to form two or three compounded noise
combinations.
4. Select adequate inner and outer arrays; assign control factors to the
inner array, and noise factors to the outer array.
5. Perform the experiment.
6. Perform statistical analysis based on S/N to identify the optimal
control factor levels. Sometimes it is helpful to conduct a control
factor–noise factor interaction study.
7. Predict optimal output performance level based on an optimal con-
trol factor level combination, and conduct a confirmation experi-
ment to verify the result.
Example 14.4 illustrates these steps.

Example 14.4. Optimization of a Purification Method for Metal-
Contaminated Wastewater (Barrado et al., 1996) Wastewater that contains