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Taguchi Methods
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18.5.2 Experimental design
Generally, the power of experimental design lies in its ability to: (i) study cause-and-
effect relations between design parameters and response with only a small amount
of experimental data; (ii) isolate and quantify the effect of each parameter on the
response; (iii) study the interaction effects among the various parameters; and (iv)
assess the statistical significance of the quantified effects. Taguchi packaged the req-
uisite studies into what he termed parameter design to achieve the above objectives,
and had them reduced to step-by-step routines simple enough to be implemented by
those without any background in statistics. Parameter design is then presented as an
intermediate stage between system design (based on engineering knowledge and tech-
nical know-how) and tolerance design (which defines tolerances for manufacturing).
Many learners, however, have regarded parameter design as the essence of Taguchi
methods.
The result of Taguchi’s packaging of experimental design is a set of ‘cookbook’pro-
cedures that involve the selection of a pattern of parameter settings from a standard
set of experimental design matrices known as orthogonal arrays, using a graphical aid
called linear graphs. 1−3 The user would not know the rationale behind the manip-
ulation of parameter settings executed during an experimental study, nor would he
be able to alter the designs to meet any practical constraints faced in the study. For
3
example, Taguchi’s L 4 (2 ) design, as given by his standard orthogonal array, is only
4
one of two possible equivalent designs; for more complex design types, such as L 9 (3 ),
there are even more possibilities unknown to the Taguchi methods user, which can be
readily constructed by those who are trained in design of experiments the traditional
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way (see Box et al. for a complete coverage of the subject, including the use of factorial
and fractional factorial designs).
For the purpose of studying noise parameters, Taguchi also advocated a procedure
inwhichonematrixcomprisingnoiseparametersisembeddedinthemainexperiment
with design parameters. These matrices are referred to, respectively, as the outer array
(since the noise parameters are external to the physical system) and the inner array
(since the design parameters are built into the physical system). With such designs,
the total number of measurements to be made could balloon considerably, draining
valuable resources (time and cost) except where experimental trials can be conducted
by computer simulation.

18.5.3 Data analysis
The possible drawbacks of the experimental design procedures outlined above are
not the major bones of contention concerning Taguchi’s parameter design. There are
serious criticisms surrounding the way in which experimental data are to be analyzed.
First, as pointed out before, traditional analysis of data from experimental design is
based on the fundamental assumption of constant variance in response; Taguchi ex-
plicitly regards response variance as variable, and no concern is expressed over the
distributional properties of data used in his formal statistical significance tests. Secondly,
Taguchi combines the level of response y with the observed variance of y in various
formats under the general label of ‘signal-to-noise ratio’, and suggests ways to opti-
mize this ratio through manipulations of design parameter values. Many have argued