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Design Optimization:Taguchi’s Robust Parameter Design 511

1 n
MSD
y i 2 (14.17)
n i 1
where MSD stands for the mean-squared deviation from the target
value 0. The signal-to-noise ratio in this case is defined as

1 n
S/N 10 log
y i 2 (14.18)
n
i 1
Clearly, S/N is 10 times the logarithm of MSD; the smaller the MSD,
the larger the S/N ratio. Therefore, for the smaller-the-better quality
loss function, maximizing S/N is equivalent to minimizing the loss
function.

14.3.3 Larger-the-better
quality characteristics
The larger-the-better quality loss function is given by
1

L(Y) kE
2
Y
If a set of observations of quality characteristic Y are given, that is,
2
y 1 ,y 2 ,…, y n , the statistical estimate of E(1/Y ) is
1 n 1
MSD
(14.19)
n i 1 y i 2

The corresponding S/N is

1 n 1
S/N 10 log
(14.20)
n 2
i 1 y i
Again, maximizing S/N is equivalent to minimizing the quality loss
function.

14.3.4 Robust parameter design using
signal-to-noise ratio and orthogonal
array experiment
In Taguchi’s robust parameter design approach, a number of design
parameters will be selected and an orthogonal array for the experi-
ment will be selected. In each experimental run, several replicates
of output performance observations will be collected as shown in
Table 14.1.