Transcript Lecture 9.1 - University of South Carolina

The Essentials of 2-Level Design of Experiments
Part I: The Essentials of Full Factorial Designs
Developed by Don Edwards, John Grego and James Lynch
Center for Reliability and Quality Sciences
Department of Statistics
University of South Carolina
803-777-7800
Part I.3 The Essentials of 2-Cubed Designs
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Methodology
– Cube Plots
– Estimating Main Effects
– Estimating Interactions (Interaction
Tables and Graphs)
Statistical Significance:
When is an Effect “Real”?
An Example With Interactions
A U-Do-It Case Study
Replication
Rope Pull Exercise
Replication
Why?

Average values have less variability as the
number of things you average increases
– Estimated effects will be reliably closer to true effects
– More of the mid-sized and small effects will be
distinguishable from error
– Data from replicated experiments can be used to
estimate the amount of variability in the process (This
allows more formal test for “real” effects—ANOVA).
– Data from replicated experiments can be used to
determine not only which factors affect the mean of
the process, but which factors affect the variability of
the process.
Replication
Analysis of a Replicated 23
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Replication means repeating the entire set of 8 runs, but (for the
analysis as described below), the entire collection of runs should be
done in random order (be it 16, or 24, or 48, etc. runs); if you want
to do them in complete sets of 8, you should analyze the results in
blocks—explained later).
For our analysis, you can reduce the data to averages over each of
the 8 treatment combinations; use these averages as your “y’s” in
the rest of the analysis.
– Discussion of shortcomings of this approach to follow
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Effects plot, interaction plots, and EMR calculations are done as
before using these estimated effects.
Replication Example to Follow!
U-Do-It Exercise
Rope Pull Study* - 23 with Replication
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Purpose of the Design
– Test Hose to Determine the Effect of
Several Factors on an Important Quality
Hosiery Characteristic, Rope Pull
– Response y = Upper Boot Rope Pull (in
inches)
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Factors:
– A: Vacuum level
(Lo, Hi)
– B: Needle Type
(EX, GB)
– C: Upper Boot Speed (1000,1200)
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Two Replicates of the Full 23 Were
Performed
*Empirical basis for this data was motivated by a much
larger study performed by the developers at Sara Lee
Hosiery
U-Do-It Exercise
Rope Pull Study - Experimental Report Form
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
std. order
Run #
5
2
1
7
3
3
6
8
4
5
6
1
7
2
4
8
Vacuum
level
Needle
Type
U.B.
Speed
LO
HI
LO
LO
LO
LO
HI
HI
HI
LO
HI
LO
LO
HI
HI
HI
EX
EX
EX
GB
GB
GB
EX
GB
GB
EX
EX
EX
GB
EX
GB
GB
1200
1000
1000
1200
1000
1000
1200
1200
1000
1200
1200
1000
1200
1000
1000
1200
Boot
rope pull
(in.)
94.8
109.8
100.3
92.1
102.3
99.2
95.4
94.7
110.1
92.7
97.6
100.4
92.7
111.9
108.3
96.2
U-Do-It Exercise
Rope Pull Study - The Analysis
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To do: Analyze the data. This should include...
– Fill in the table on the next slide.
– Analyze the averages in Minitab:
 Create a 3-factor 2-level design, enter the averages as
a response variable; compute factor effects and
construct a normal probability plot of the effects.
 If appropriate, graph interaction plots.
 Compute EMR using only the significant terms
U-Do-It Exercise
Rope Pull Study - The Analysis
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
std. order
Run #
5
2
1
7
3
3
6
8
4
5
6
1
7
2
4
8
Vacuum
level
Needle
Type
U.B.
Speed
LO
HI
LO
LO
LO
LO
HI
HI
HI
LO
HI
LO
LO
HI
HI
HI
EX
EX
EX
GB
GB
GB
EX
GB
GB
EX
EX
EX
GB
EX
GB
GB
1200
1000
1000
1200
1000
1000
1200
1200
1000
1200
1200
1000
1200
1000
1000
1200
Boot
rope pull
(in.)
94.8
109.8
100.3
92.1
102.3
99.2
95.4
94.7
110.1
92.7
97.6
100.4
92.7
111.9
108.3
96.2
Stardard
Order Run
#
1
2
3
4
5
6
7
8
First y
Second y Average