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Design Optimization:Taguchi’s Robust Parameter Design 509

characteristic for many circuits or products. Taguchi, whose back-
ground is communication and electronic engineering, introduced the
same concept in many earlier designs of experiment projects in Japan.

14.3.1 Nominal-the-best quality
characteristics
In communication engineering, Fig. 14.9 is a typical representation of
how the system works.
In a typical communication system, if an input signal is given, then
an output signal y should be produced by the system. In an ideal situ-
ation, if there is no noise input, the output y will be consistent and
have no variation. However, with noise input, the output y will not be
consistent and will vary. For a good communication system, the noise
effect should have minimal influence in comparison with the output y;
therefore, the following signal-to-noise ratio (S/N) is often used as a
quality characteristic of a communication system:

Signal power 2
(14.11)
Noise power 2

where E(Y), Var(Y). The larger the ratio given by Eq. (14.11),
2
the more desirable the communication is. In communication engineer-
ing, the signal-to-noise ratio is actually 10 times the logarithm of the
ratio in Eq. (14.11):

2

S/N 10 log 2 (14.12)

Use of a logarithm of a signal-to-noise ratio is based on the fact that the
logarithm will transform a multiplicative relationship into an additive
relationship; thus the logarithm transformation will “smooth out” lots
of nonlinearities and interactions, which is desirable in data analysis.
In real-world conditions, both and can only be estimated statis-
2
tically. If a set of observations of quality characteristic Y are given,
that is, y 1 ,y 2 ,…,y n , the statistical estimate for is

Signal
input Output
System Desired quality characteristic y

Noise

Figure 14.9 A typical communication system.