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In a Taguchi design, the name used for
the design array that contains the controllable
factors, as opposed to the Outer Array that
contains the noise factors. See Outer Array
for a more complete description.
Linear graphs are used to
help allocate the appropriate columns of
a Taguchi array to the factors and interactions.
The figures show two alternative linear
graphs for the L8 design:
Column 3 contains the interaction between
columns 1 and 2.
Column 1 contains few sign level changes.
The circles are coded to distinguish the
columns that have many level changes from
those with few changes. If it is difficult
to change the level of one of the factors,
column 1 would be a good choice, and column
4 a poor choice (Taguchi designs are not
usually randomized).
See Taguchi Loss Function
Taguchi distinguishes between 'noise' factors
and 'controllable' factors. Noise factors
are those that cannot be controlled in normal
operation, but can be controlled for the
purpose of testing. An example is shown
below. The experiment is to find the best
values for the three design features in
a relief valve: Hole Size, Spring Length
and Ball Size. The noise factors are the
Oil Temperature and Water Vapor Pressure.
| |
Outer
Array |
| D
Oil Temperature |
1 |
2 |
1 |
2 |
|
| E
Water Vapor Pressure |
1 |
1 |
2 |
2 |
|
| |
Inner
Array |
|
|
|
|
|
| |
A
(hole) |
B
(spring) |
AB |
C
(ball) |
AC |
BC |
- |
|
|
|
|
|
| Run |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
|
|
|
|
S/N
Min |
| 1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
44.9 |
51.9 |
52.6 |
59.9 |
-34.42 |
| 2 |
1 |
1 |
1 |
2 |
2 |
2 |
2 |
102.0 |
113.5 |
125.0 |
99.0 |
-40.86 |
| 3 |
1 |
2 |
2 |
1 |
1 |
2 |
2 |
47.3 |
51.3 |
54.1 |
61.1 |
-34.60 |
| 4 |
1 |
2 |
2 |
2 |
2 |
1 |
1 |
111.0 |
103.0 |
104.0 |
127.5 |
-40.97 |
| 5 |
2 |
1 |
2 |
1 |
2 |
1 |
2 |
157.8 |
157.2 |
154.3 |
165.2 |
-44.01 |
| 6 |
2 |
1 |
2 |
2 |
1 |
2 |
1 |
188.5 |
194.0 |
211.5 |
197.5 |
-45.94 |
| 7 |
2 |
2 |
1 |
1 |
2 |
2 |
1 |
148.6 |
159.5 |
198.0 |
176.7 |
-44.70 |
| 8 |
2 |
2 |
1 |
2 |
1 |
1 |
2 |
220.0 |
198.5 |
217.5 |
220.0 |
-46.62 |
| S/N
avg @ 2 |
-45.31 |
-41.72 |
-41.38 |
-43.59 |
-42.63 |
-41.52 |
-41.52 |
|
|
|
|
|
| S/N
avg @ 1 |
-37.71 |
-41.31 |
-41.65 |
-39.43 |
-40.39 |
-41.50 |
-41.51 |
|
|
|
|
|
| D
S/N |
-7.60 |
-0.41 |
0.27 |
-4.16 |
-2.24 |
-0.02 |
-0.01 |
|
|
|
|
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A robust process is one that is insensitive
to variation and thus gives consistent quality.
The Taguchi approach is aimed at achieving
robust processes.
One idea is that 'control factors' and
'noise factors' that can be identified during
the design stage. The design can be configured
to select the control factor combinations
that minimize the noise (see the Signal
to Noise' ratio.
Another idea is that variation can be costed
through the Taguchi Loss Function.
The design process has three stages:
- system design: use scientific and engineering
principles to create a prototype
- parameter design: find the settings
for the product and process parameters
to minimize variation
- tolerances: set tolerances on the control
parameters to minimize the loss
Taguchi proposed using 'Signal to Noise'
ratios to optimize processes. The idea is
that the best process settings are those
that maximize the signal to noise ratio.
If the requirement is to [maximize/minimize]
the response then maximizing the signal
to noise ratio may not achieve the [highest/lowest]
value that can be attained if process variation
is ignored. It does however give the [highest/lowest]
average value when variation is taken into
account.
If the requirement is to achieve a target
response, maximizing the signal to noise
ratio will give the factor settings that
achieve the target response with least variation.
The signal to noise ratios are:
Minimize
the Response |
Maximize
the Response |
Achieve
a Target |
|
|
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Taguchi developed a series of arrays for
use with Taguchi Designs. These are designated
Ln arrays, where 'n' is the number
of runs.
The columns in these arrays are highly
confounded. They are generally used as screening
designs, with only selected interactions
investigated. A feature of these arrays
is that the two way interactions have the
signs reversed; if A and B are both +1,
then AB would be -1. The arrays include
two, three, four, and mixed level designs.
Taguchi designs are a type of experimental
design pioneered by Genichi Taguchi. They
are distinguished by the use of:
- the Signal to Noise Ratio
- inner and outer arrays
- Taguchi arrays
Taguchi designs are criticized by many
experts. Taguchi does not give the same
attention to interactions (taguchi designs
are often highly confounded screening
designs)
as the classical design of experiment approach.
It is also easy to demonstrate that the
Signal to Noise ratio method does not always
give the best results, particularly when
the aim is to achieve a target response
rather than maximize or minimize the response.
One of the original advantages of the Taguchi
approach was that it favored graphical
analysis
and avoided complex analysis. With modern
software, such as Minitab, this advantage
is no longer as strong.
Taguchi challenged the view that anything
within specification was good product, and
needed no action. He asserted that any deviation
from the target was a 'loss to society'
in reduced life expectation, utility etc.
He proposed that the loss
function could be represented by a quadratic
where:
For the process output this
gives:
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