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Taguchi’s ‘Statistical Engineering’ 277
that with this method, opportunity is lost to adjust the parameters to suit two distinct
sets of objectives, one in response level and one in response variation. Thus it has
been suggested that with reference to Figure 18.6, in terms of equation (18.1), y I and
2
y II could represent y and σ , respectively, and an investigator could determine suitable
values of x 1 , x 2 , x 3 to meet separate objectives in level and variation control. 11,17,18
Third, and more important, is the way in which parameter values are matched to
Taguchi’s orthogonal arrays for experimentation. Since the user of standard arrays is
not aware of the rationale of their construction, it is difficult for him to understand the
extent of confounding, that is, the mixing up of multiple parameter interactions with
single-parameter effects, in his data analysis. An unsuspected interaction between
two or more parameters could grossly distort the conclusion to be drawn from the
analysis. The orthogonal arrays for parameters set at three levels, a popular choice of
Taguchi methods users, can yield particularly misleading results. Such problems are
compounded by the availability in recent years of purportedly user-friendly Taguchi
methods software packages; many such packages ‘automatically’select an orthogonal
array, assign parameters to the columns, spew out a barrage of statistics and graphical
displays, then point to a single ‘best’ solution, all with minimal intervention from the
user.
Fourthly, in an effort to present an easy-to-follow data analysis procedure, instead
of structuring a valid mathematical model for the overall input--output relationship,
a routine is advocated whereby the effects of single parameters are examined one
at a time, and recommended settings picked directly according to objectives such as
response maximization or minimization. Such a simplistic approach, also referred
to as marginal analysis or simply ‘pick the winner’, has been pointed out time and
again 12,13 to be apt to lead to false results: this will be illustrated later in this section.
Taguchi methods advocates have always defended the routine by stressing that all
recommended settings are to be tested in a final confirmation experiment. However,
there is no guarantee that an improved performance obtained during the confirmation
experiment is indeed the best achievable, and no satisfactory suggestion has been
put forward as to what is to follow if the confirmation experiment turns out to be
unsatisfactory. Indeed, the question Barbra Streisand asked ruefully in the song ‘The
Way We Were’ would not be out of place under such circumstances: ‘If we had the
chance to do it all again . . . would we? could we?’ The answer is likely to be ‘no’,
since an ordinary Taguchi methods user, not having the capability to decipher the
complete confounding pattern of interactions hidden in the orthogonal array used for
his experiment, would find it impossible to try any other orthogonal array to probe
the governing cause-and-effect mechanism in the subject of study.
A further objection to marginal analysis is that the recommended solution is con-
fined only to the very parameter settings that have been used in the experimental
trials; in practice, parameter fine-tuning on a range can be readily accomplished once
valid mathematical models are established. 36
In addition, Taguchi methods users generally do not have the means to break away
from the experimental region to seek new parameter settings that could further opti-
mize the desired performance, or to refine existing settings to suit changing operating
conditions. Statisticians, in contrast, have on hand established strategies such as re-
sponse surface methodology and evolutionary operation for such purposes. (For an
illustration of response surface methodology applications that can never be carried