Presented by Dr. Neil W. Polhemus screening designs...Statistics for Experimenters: An Introduction...
Transcript of Presented by Dr. Neil W. Polhemus screening designs...Statistics for Experimenters: An Introduction...
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Definitive Screening Designs
Presented by
Dr. Neil W. Polhemus
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Definitive Screening Designs
• A class of statistically designed experiments that
may be used for both screening and optimization.
• Handle both quantitative and categorical factors.
• Quantitative factors are run at 3 levels, which
allows the estimation of both linear and quadratic
effects.
• First described by Bradley Jones and Christopher
Nachtsheim in a 2011 article in the Journal of
Quality Technology.
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Properties
1. The required number of runs is very small, usually between 1 and 3 more than twice the number of factors.
2. Main effects are independent of two-factor interactions.
3. Two-factor interactions are not perfectly confounded with other two-factor interactions, although they are correlated.
4. For continuous factors, all of the quadratic effects can be estimated.
5. Quadratic effects are orthogonal to linear main effects and only partially confounded with two-factor interactions.
6. For designs involving 6 through 12 factors, the full second-order model can be estimated for any 3 or less factors.
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DOE Wizard
• The Statgraphics DOE Wizard provides DSDs for
any combination of 4 to 16 factors.
• Both blocked and unblocked designs are available.
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Example #1
• Optimization of a chemical reaction from Statistics for
Experimenters by Box, Hunter and Hunter (2005).
• Response variable Y: percent reacted
• Experimental factors:
– X1: feed rate
– X2: amount of catalyst
– X3: agitation rate
– X4: temperature
– X5: concentration
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Step 1: Define Responses
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Step 2: Define Experimental Factors
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Step 3: Select Design
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Step 3: Select Design (cont.)
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Step 3: Select Design (cont.)
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Step 3: Select Design (cont.)
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Step 4: Specify Model
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Step 5: Select Runs
• Not required since the design already has the
desired number of runs. This step is used for a
computer generated design (such as a D-optimal
design) when a subset of a large set of candidate
runs needs to be selected.
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Step 6: Evaluate Design
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Step 6: Evaluate Design (cont.)
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Step 6: Evaluate Design (cont.)
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Step 6: Evaluate Design (cont.)
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Step 6: Evaluate Design (cont.)
10
15
1
2
100
120
140
180
3
6
feed rate
catalyst
agitation
temperature
concentration
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Step 6: Evaluate Design (cont.)
Prediction Variance Plot
agitation=110.0,temperature=160.0,concentration=4.5
10 11 12 13 14 15feed rate
11.2
1.41.6
1.82
catalyst
0
0.2
0.4
0.6
0.8
1
Stn
d.
err
or
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Step 6: Evaluate Design (cont.)
FDS Plot
(cuboidal region)
0 0.2 0.4 0.6 0.8 1
Fraction of design space
0
3
6
9
12
15
Sc
ale
d p
red
icti
on
va
ria
nc
e
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Step 7: Save Experiment
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Step 8: Analyze Experiment
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Pareto Chart of Effects
Standardized Pareto Chart for reacted
0 2 4 6 8 10
Standardized effect
C:agitation
EE
A:feed rate
AA
CC
BB
E:concentration
DD
D:temperature
B:catalyst +-
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Collapse Design
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Pareto Chart for Collapsed Design
Standardized Pareto Chart for reacted
0 3 6 9 12 15 18
Standardized effect
BB
EE
BE
BD
DE
E:concentration
DD
D:temperature
B:catalyst +-
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Main Effects Plot
catalyst
1.0 2.0
temperature
140.0
Main Effects Plot for reacted
68
73
78
83
88
93
98re
acte
d
180.0
concentration
3.0 6.0
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Interactions Plot
Interaction Plot for reacted
59
69
79
89
99re
acte
d
BD
1.0 2.0
-
-
+
+
BE
1.0 2.0
-
-
+
+
DE
140.0 180.0
-
-
+
+
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Mesh Plot
Estimated Response Surface Meshfeed rate=12.5,agitation=110.0
1 1.2 1.4 1.6 1.8 2catalyst
140150
160170
180
temperature
3
3.5
4
4.5
5
5.5
6
co
ncen
trati
on
reacted56.061.066.071.076.081.086.091.096.0101.0106.0
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Step 9: Optimize Responses
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Step 9: Optimize Responses (cont.)
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Designs with Categorical Factors
• DSDs may also contain 2-level categorical factors.
• The next example shows a design with 4
continuous factors and 2 categorical factors.
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Example #2
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Example #2 (cont.)
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Example #2 (cont.)
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Designs with Blocking
• DSDs may be run in more than one block.
• The next example shows a design with 6
continuous factors divided into 2 blocks.
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Example #3
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Example #3 (cont.)
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Example #3 (cont.)
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References
StatFolios and data files are at: www.statgraphics.com/webinars
Articles:
Box, G. E. P., Hunter, W. G. and Hunter, J. S. (2005). Statistics for Experimenters: An
Introduction to Design, Data Analysis, and Model Building, 2nd edition. New York: John Wiley
and Sons.
Jones, B. and Nachtsheim, C.J. (2011) “A Class of Three-Level Designs for Definitive Screening
in the Presence of Second-Order Effects”, Journal of Quality Technology 43(1), pp. 1-15.
Jones, B. and Nachtsheim, C.J. (2013) “Definitive Screening Designs with Added Two-Level
Categorical Factors”, Journal of Quality Technology 45(2), pp. 121-129.
Jones, B. and Nachtsheim, C.J. (2016) “Blocking Schemes for Definitive Screening Designs”,
Technometrics 58(1), pp. 74-83.
Xiao, L., Lin, D.K.J. and Bai, F. (2012) “Constructing Definitive Screening Using Conference
Matrices”, Journal of Quality Technology 44(1), pp. 1-7.