# Quality Progress - February 2018 - 27

as possible, it is the case of smaller-the-better. In this case, the S/N
ratio is the negative log function of
the average output square:
1 n
S/N = −10 log _ ∑ yi2
n i=1
Where n = the number of output
yi (i = 1, 2, ... n).
If the control system output must
be as large as possible, it is the case
of larger-the-better. In this case, the
S/N ratio is the negative log function
of the average of the reversed output square:
1 n _
1
S/N = −10 log _ ∑
n i = 1 yi2

to adjust the A/B ratio. Because this design
reduces the number of valves from two to one,
it reduces the number of variables in the control
system. Therefore, not only does the design
satisfy the independence axiom, it also satisfies
axiom two by reducing the control system's
complexity.

Taguchi robust parameter design
Taguchi robust parameter design, another
DFSS crown jewel, is a systematic method that
applies DoE to optimize designs by enhancing
their transfer functions. It greatly improves the
fundamental functions of engineering systems
by maximizing the signal-to-noise (S/N) ratio,
which compares the power of an engineering
system's desired signal to the power of the
background noise.

(

)

(

)

Taguchi robust
parameter design,
another DFSS crown
jewel, is a systematic
method that applies
DoE to optimize
designs by enhancing their transfer
functions.

Design optimization

For the smaller-the-better and the larger-the-better cases, the optimization strategy
is simply to maximize the S/N ratio. For the
nominal-the-best case, however, there are two
steps involved in optimization, as illustrated in
Figure 6.
The first step is to find and adjust the significant DPs to maximize the S/N ratio. The
significant DPs are those that have a significant
effect on the S/N ratio.
The second step is to find and adjust the
mean adjustment DPs to move the mean
response to the target. The mean adjustment
DPs are those that do not have a significant
effect on the S/N ratio but have a significant

Three S/N cases

For an engineering system to function effectively, the S/N ratio must be as large as possible.
If the control system output must be at the
target, it is the case of nominal-the-best. In this
case, the S/N ratio is the logarithm of the ratio
of average output to standard deviation:
y
S/N = 20 log _
s
Where S = the power of the control system
signal, N = the power of the background noise, y
= the average of the control system output and
s = the variation of the control system output.
If the control system output must be as small

()

FIGURE 6

Two-step optimization strategy
S/N ratio

Target

Target

Step 1

-5.0 -2.5 0.0 2.5 5.0
DP

Target

Step 2

-5.0 -2.5 0.0 2.5 5.0
DP

-5.0 -2.5 0.0 2.5 5.0
DP

DP = design parameter S/N = signal to noise

qualityprogress.com ❘ February 2018

QP 27

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Seen and Heard
Progress Report
Career Coach
Office Efficiency
The Crown Jewels of Design
Open Lines
Less Is More
ASQ 2018 Six Sigma Resource Guide
Standard Issues
Six Sigma Solutions
Statistics Spotlight
Marketplace
Footnotes
Try This Today
Quality Progress - February 2018 - intro
Quality Progress - February 2018 - cover1
Quality Progress - February 2018 - cover2
Quality Progress - February 2018 - 1
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Quality Progress - February 2018 - Progress Report
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Quality Progress - February 2018 - Mr. Pareto Head
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Quality Progress - February 2018 - ASQ 2018 Six Sigma Resource Guide
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Quality Progress - February 2018 - Standard Issues
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Quality Progress - February 2018 - Six Sigma Solutions
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Quality Progress - February 2018 - Statistics Spotlight
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Quality Progress - February 2018 - Marketplace
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