Page 267 - Six Sigma Advanced Tools for Black Belts and Master Black Belts

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JWBK119-16
252 A Glossary for Design of Experiments with Examples
Noise Factors
... Z
Z 1 n
Control Factors
X 1
Mean, μ
... ... Process
X k Variance, s 2
Figure 16.12 Taguchi DOE model.

(Table 16.10). Repeats are back-to-back measurements of a response at fixed factor
levels. Replicates are independent runs conducted at identical sets of factor levels,
in which all sources of inherent variation are present. Repeat measurements are not
replicated runs because differences among such measure values do not include all
sources of inherent variation.
It is not mandatory that the number of replicates equal the number of blocks re-
quired. However, the number of replicates should be sufficient to avoid confounding
of the main effects and two-way interactions. Consider the example in Table 16.9 with
3 control factors and 3 noise factors (with 4 blocks). Replicates might be applied as
shown in Table 16.11.

16.6.5 Determining repeats and replicates

16.6.5.1 Repeated measures
The standard deviation (and corresponding variance) determined within a run (or
2
treatment) is the sample standard deviation s (and corresponding sample variance s ). It

Table 16.9 A design with three control factors and three noise factors.

OA of noise factors
Z 1 −1 +1 −1 +1
Z 2 −1 −1 +1 +1
IA of control factors Z 3 +1 −1 −1 +1
Run A B C AB AC BC ABC y 1 y 2 y 3 y 4 Mean Variance
1 −1 −1 −1 +1 +1 +1 −1 s 2
y 1
1
2 +1 −1 −1 −1 −1 +1 +1 s 2
y 2
2
3 −1 +1 −1 −1 +1 −1 +1 y 3 s 2
1 2 3 4 3
4 +1 +1 −1 +1 −1 −1 −1 Block Block Block Block y 4 s 4 2
5 −1 −1 +1 +1 −1 −1 +1 s 2
y 5
5
6 +1 −1 +1 −1 +1 −1 −1 y 6 s 6 2
7 −1 +1 +1 −1 −1 +1 −1 y 7 s 7 2
8 +1 +1 +1 +1 +1 +1 +1 y 8 s 8 2