Chapter 8 Robust Designs. C. S. R. O. R. Robust Designs. Focus : A Few Primary Factors Output : Best/Robust Settings. C. S. R. O. R. I/O Arrays Assembled Designs. Robust Designs. Robust Experimentation.
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Most automotive subassemblies like the alternator, the ignition coil, and the electronic control module must undergo testing to determine if they are resistant to salt water that may be splashed on them from the read. An automotive supplier is testing an ignition coil to determine if it will withstand salt water. The following factors are tested:
The signal to noise ratio confounds the mean and the variance together and assumes that the variance is proportional to the mean.
The signal to noise ratio does tend to prefer combinations of levels that decrease noise and are on target, but assumes that the variance is proportional to the mean.
If it isn’t, then the method gives an unknown compromise.
The signal to noise ratio again confounds the mean and the variance together and assumes that the variance is proportional to the mean.
2 represents measurement error
2 represents measurement and setup error
2 represents variance expected in the field due to field conditions and measurement and setup error. The idea of robustness is to set the x’s to minimize the variance, while keeping the average response at a desired level.
2 represents variance expected in the field and measurement and setup error.
The purpose of each of these configurations is to reduce the experimental cost and target certain effects to have higher precision of measurement.
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4
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Control by Noise Factor InteractionsInteraction between Shortening and Temperature
Shortening
Moistness
Set Control Factor
(e.g. Shortening) to
Low Level
Noise Factor (e.g. Temp.)
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n
a
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M
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Control by Noise Factor InteractionsInteraction between Flour and Temperature
Flour
Moistness
Set Control Factor
(e.g. Flour) to
Middle Level
Noise Factor (e.g. Temp.)
0

1
5
0
1
n
a
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0
M
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Control by Noise Factor InteractionsInteraction between Egg and Temperature
Egg
Moistness
Set the Adjustment
Factor (e.g. Egg) to
Set Mean on Target
Noise Factor (e.g. Temp.)
Notice that as long as each individual array is Resolution III the shortest word containing both control and noise factors will have length 6.
Control by Noise Factor Interactions will be confounded with interactions of order Min(RC, RN). So, if both arrays have Resolution III then CxN interactions will be confounded with three factor interactions.
8
5
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3
4
1
2
Assembled DesignsA class of experimental design for estimating location effects,
dispersion effects, and variance components.
Parameters:
r = # of Design Points
n = # of observations per Treatment Combination (assume constant)
s = # of different structures used in the design
BT = total number of Batches
r = 8
n = 4
s = 2
BT = 20
x2
x3
x1
“Works for anything that involves making batches and taking observations”
Must have design points ordered in some way.
Notation for Assembled DesignsExample: 23 design, Splitting Generator = ABC, r=8, s=2, B1=4, B2=3, n=6