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Design Optimization:Taguchi’s Robust Parameter Design 503

quality loss is symmetric on either side of the target value. This type
of quality characteristic is called nominal-the-best (meaning “nominal
is best”). An example is TV set color density (Example 14.1).
The following quality characteristics require different types of qual-
ity loss functions:
■ Smaller-the-better quality characteristics. For some quality charac-
teristics, such as percentage defect rate or radiation leakage from a
microwave oven, the ideal target values are zero. Other examples of
such quality characteristics, termed smaller-the-better (i.e., “the
smaller, the better” or “smaller is better”), are response time of a
computer, leakage current in electronic circuits, and pollution from
automobile exhaust. The quality loss function in such cases can be
obtained by letting T 0 in Eq. (14.3).
L kEY 2 (14.5)

■ Larger-the-better quality characteristics. For some quality charac-
teristics, such as welding bond strength, the ideal target value is
infinity. These are larger-the-better (i.e., “the larger, the better” or
“larger is better”) quality characteristics. Performance level will pro-
gressively worsen if y decreases; the worst possible value is zero. It
is clear that the behavior of this characteristic is the reciprocal of or
inversely proportional to that of the smaller-the-better characteristic.
Thus, we can substitute 1/Y in Eq. (14.5) to obtain the quality loss
function in this case:

1
L kE 2 (14.6)
Y
■ In this case, if the functional limit is 0 , below which the product will
fail and the replacement or repair cost is A 0 , then, by Eq. (14.6), k can
be determined as

2
k A 0 0 (14.7)
These three kinds of quality characteristics and their loss functions
are plotted in Fig. 14.4.

Components of quality loss. Without losing the generality, we use the
nominal-the-best quality loss function in Eq. (14.3) to get

2 2 2 2
L kE(Y T) k( y T) k Var(Y) k( y T) k y (14.8)
where y E(Y), which is the mean value of performance level Y, and
Var(Y) is the variance of performance level Y.