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Robust Design 251
LSL USL
Loss

Target
Performance Measure

Figure 16.10 Illustration of quadratic loss function.

16.6.2 Classical DOE model vs. Taguchi DOE model
The classical design experiments model is illustrated in Figure 16.11, while the Taguchi
DOE model is shown in Figure 16.12. Under the Taguchi model, appropriate treat-
ments (combinations of control factors) may be determined to obtain the optimal mean
2
(μ) and/or minimal variance (σ ) in the response. Control factors are product design
or process factors that influence a product’s performance, and may be controlled by
the designer or manufacturer (e.g. electrical parameters, component dimensions).
The recommended treatment should be robust enough against the effects of the
noise factors. These are variables that affect a product’s performance, but whose val-
ues cannot be controlled by the designer or manufacturer or are not controlled for
economic reasons (e.g. raw material, equipment condition, labor skill, environment).

16.6.3 Taguchi’s inner and outer arrays
The effects of noise factors may be included in an experimental design via blocking.
Blocking an experiment is arranging the runs of the experiment in groups (‘blocks’)
so that runs within each block have as much extraneous variation in common with
each other as possible, -- examples are using material from the same lot, evaluation
under the same machine/line, and carrying out runs within a short time frame.
To accommodate both control factors and noise factors, Taguchi’s design consists
of two parts: an inner array (IA), a design involving only control factors; and an outer
array (OA), a design involving only noise factors. Table 16.9 shows an example of a
design with three control factors and three noise factors.

16.6.4 Repeats and replicates

An estimate of the random error (in a classical DOE model) or process variability (in a
Taguchi DOE model) may be obtained by repeated measurements and/or replicated runs

2
Noise ∼ NID(0,s )
Factor, X 1
… … Process μ r Response, Y i
Factor, X k

Figure 16.11 Classical DOE model.