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Taguchi’s ‘Statistical Engineering’ 275
x 4 x 5
(iii)
x 1 y
x 2 P σ 2
x 3
(ii) (i)
Figure 18.6 Taguchi’s model of noise effects.

distributed, has no long-term systematic value, but is characterized by a constant
variance:
2
e ∼ N 0,σ . (18.3)
2
Hence y is subject to a constant variance σ whenever the values of parameters x 1 , x 2 ,
x 3 are fixed.
Such a model has been used by statisticians for design of experiments for a long
time, and formed the basis of work by Box and others 28−35 before the advent of Taguchi
methods. Taguchi’s model is typified in Figure 18.6. It differs from the previous one
2
in at least three ways: (i) The variation in response, reflected by σ , is not constant;
instead, it is considered a function of design parameters x 1 , x 2 , x 3 . (ii) Such parameters
do not necessarily stay at the set (nominal) values during the actual operation of a
product or process as is desired and commonly assumed. (iii) Certain external noise
parameters (say x 4 , x 5 ) can be, where possible (e.g. by simulation), included in the
study of design parameters (x 1 , x 2 , x 3 ) so that the latter can be optimized with a view
to counteracting the effects of the former .
From an engineering point of view, the above features do add realism to prob-
lem formulation, as (i) consistency, not just the average, of response can sometimes
be directly influenced by design choice, such as the amount of pressure used in an
assembly process, or the type of material used in a product; (ii) the nominal value
recommended for a product or process is not necessarily what is realized; for exam-
ple, there is always piece-to-piece variation of the actual resistance value of a resistor
specified for a product and, in the case of a process, what is actually found in an oven
often does not correspond to the nominal temperature setting; (iii) parameters such as
environmental temperature and humidity can and should be simulated at the design
and development stage to expose possible weaknesses in a product or process; ways
should then be found to improve both the level and variation of y through judicious
adjustments of design parameters.
It is useful to note that the impact of noise is traditionally regarded as inevitable
but uniform in statistical design of experiments, which is a reasonable assumption
in agricultural experiments because weather and other natural elements do exert a
consistent influence over all the plants under study. Taguchi, however, treats variation
in response as a subject of study in itself: this again is understandable because noise
is the very source of quality and reliability problems; not only should it be recognized
and assessed, but also efforts should be made to remove or neutralize it where possi-
ble. This idea then leads to yet another difference between Taguchi and mainstream
statisticians, in the way experiments are designed.