Page 561 - Design for Six Sigma a Roadmap for Product Development

Design Optimization:Taguchi’s Robust Parameter Design 519

combination. For example, in the first run of inner array in Table 14.4,
, where each observation corresponds to the same
we get y 11 ,y 12 ,…,y 1N 2
control factor level combination but different noise factor level combi-
is clearly caused by noise
nations, so the variation among y 11 ,y 12 ,…,y 1N 2
factors. S/N will be computed for each run of inner array; clearly, a
higher S/N indicates less sensitivity to the effects of noise factors.
Therefore, the optimal design parameter selection based on this kind
of experimental study will have a far better chance to be robust in per-
formance in real-world usage.
In many robust parameter design projects, because of the high cost
of building the actual hardware prototypes, computer simulation
models are used instead of real tests. In these projects, design para-
meters are varied in computer models and output responses are sim-
ulated by the computer. In this situation, S/N calculated as described
2
in Sec. 14.3 will not work because the variation s from a group of
replicated output response observations will always be zero.
Therefore, noise factors must be introduced for computer-simulated
robust parameter design.
It is desirable to introduce a sufficient number of noise factors in
robust parameter design to ensure future performance robustness
toward many kinds of noise factors. However, if we use the inner/
outer-array approach, the more noise factors we introduce, the larger
the outer array will be, and the larger N 2 will be. In Table 14.4, it is
clear that the total number of output response observations y ij is equal
to N 1
N 2 ; when N 2 increases, N 1
N 2 will be too high.
In order to reduce the number of experimental runs, Dr. Taguchi
proposed a “compounded noise factor” strategy for introducing noise
factors. Taguchi stated that to estimate the robustness indicated by
signal-to-noise ratio, we do not need to run all possible noise combina-
tions designated by the outer array. If a product design is robust
toward a small number of extreme or “worst” noise factors level com-
binations, it will probably be robust to all “minor” or benign noise fac-
tor level combinations. The compounded noise factors means to find
two extreme combinations of noise factors:

N1 negative-side extreme condition
N2 positive-side extreme condition

Or three combinations:

N1 Negative-side extreme condition
N2 Standard-side condition
N3 Positive-side condition