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Design Optimization: Advanced Taguchi Robust Parameter Design 545

1. An ideal function is directly related to the main transformation
process of the main function of the technical system under study.
Sometimes it is impossible to measure the transformation directly; the
things measured in ideal functions are directly related to this trans-
formation. For example, case 2 of Example 15.2, the operational ampli-
fier, clearly is an energy transformation process; the output that we
measured is the output voltage, which is not energy, but clearly that
input voltage–output voltage relationship is a direct surrogate of this
energy transformation.
2. If a system is robust in delivering its ideal function, that is, if the
actual input-output relationship is very close to the ideal function and
has very low variation under the influence of the noise factors, for
example, such as in the case indicated in Fig. 15.6b, then it indicates
the following:

a. The transformation process is repeatable and robust at different
levels of transformation, with the presence of noise factors. For
example, for an energy transformation, the process is robust at
high, low, and mid energy levels.
b. The controllability of the transformation process is robust. If we
change the signal, the transformation process will respond with high
precision and high repeatability, even in the presence of noise factors.

How to identify and define the ideal function. Given a technical system,
we can follow the following step-by-step guidelines to identify and
define the ideal function:

1. Identify the main function of the system. If it is hard to identify, draw-
ing a functional diagram similar to Figs. 15.3 and 15.4 may help.
2. Identify the main type of transformation behind the main function;
again, if it is hard to identify, drawing a functional diagram may help.
3. Identify the “control signal” for the main transformation; usually it
is very rare that the transformation is uncontrolled in a man-made
technical system.
4. Identify the measurable input and output, where input should be
the control signal itself or a direct surrogate, and the output should
be directly related to the magnitude of transformation. Sometimes
we have to install additional measurement devices to measure
input and output.
5. Identify the ideal linear relationship between output and input.
Clearly, for any product or technical system, achieving robustness in
delivering its ideal function is highly desirable. Dr. Taguchi developed