1. Introduction to Design of Experiments
UA College of Engineering
Introduction to Design of Experiments
Brian Cunningham
Jennifer Horner

2. Short History: Design of Experiments (DOE)
Agenda
Short History: Design of Experiments (DOE)
How to use DOE to optimize the design of a spinning parachute
In-Class DOE activity with your team

3. DOE: A Short History
Design of Experiments (DOE) was first introduced in the 1920s when a scientist at an agricultural research station in England, Sir Ronald Fisher, showed how valid experiments could be conducted in the presence of many naturally fluctuating conditions such as temperature, soil condition, and rainfall.
In the past decade or two, the application of DOE has gained acceptance in the U.S. as a valuable tool for improving the quality of goods and services.
Sir Ronald Fisher

4. Design of Experiments Examples
A plastic molding workshop wants to reduce injection molding rejects; performs a set of experiments which change injection pressure, mix temperature and setting time.
Analysis of the results shows a combination of temperature and setting time as the most significant factor.
Further experiments find the optimum combination of these.

5. Design of Experiments Examples
A yacht design team aims to improve speed through changing the shape of the boat's sail.
Rather than try random shapes, they identify the key sail parameters and then design and perform a set of experiments with each factor set at two levels.
They follow this up with multi-level experiments for the two most significant factors found in the first experiment set.
The result: a new sail that increases speed by 5%.

6. Why DOE?
Minimize time and cost required to obtain the most information possible at the earliest possible stage in a product’s life cycle $
Cost of changes
To product design
time
Preliminary design
Detailed
design
Production
Consumption

7. The Spinning Parachute Company
Current best-selling model:
Fold forward
Fold backward
cut
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8. The Spinning Parachute Company
The Spinning Parachute Company wants to improve this product
Better customer satisfaction ratings
Improved sales
Goal: Improve in-flight time (fall time)

9. The Spinning Parachute Company
Preliminary research: 3 main factors impact the flight time
Blade width
Blade length
Body length
Blade width
Fold forward
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cut
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Blade length
Body length

10. The Spinning Parachute Company
P-Diagram* to represent the design improvement of the Spinning Parachute
Blade width
Blade length
Body length
Increase average fall time
Decrease standard deviation of fall time
Process
Noise
“Performance characteristics”
“Factors”
* P-diagram is short for Parameter diagram

11. The Spinning Parachute Company
Purpose of DOE in this example:
Uncover statistical relationships that connect design factors to performance characteristics
Allow the design team to select the factor settings that generate the desired performance

12. The Spinning Parachute Company
The company’s engineers want to test new dimensions for the three factors:
Wider blade
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cut 1 2
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Longer blade
Longer body

13. The Spinning Parachute Company
There are 23, or 8, possible configurations to examine:
Combination
A, Blade Width
B, Blade Length
C, Body Length 1 2 3 4 5 6 7 8
This is called a “full factorial analysis.”

14. The Spinning Parachute Company
Rather than gather the data for all eight combinations, you can obtain valuable information from considering just four carefully chosen combinations: B A
(2, 2, 1)
(1, 2, 2) C
(1, 1, 1)
(2, 1, 2)

15. Two Orthogonal Sets of Four Combinations1 2 3 4
Set 1
Combination A B C 1 2 3 4
Set 2
Each set is called a “half factorial analysis.”

16. Orthogonal Set 1 Applied to the Spinning Parachute
Combination A B C 1 2 3 4
Combination A
Blade width B
Blade length C
Body length 1
narrow
short 2
long 3
wide 4
Note that for each factor, each level is tested in two combinations

17. Gather Data for Ten Replicates
Use Set 1, the four half-factorial combinations (treatments)
Combination 1 2 3 4
(A, B, C)
(1, 1, 1)
(1, 2, 2)
(2, 1, 2)
(2, 2, 1)
1.22
1.69
1.63
1.78
1.59
1.50
1.12
1.53
1.56
1.84
1.15
1.62
1.54
1.75
1.25
1.60
1.28
1.19
1.72
1.38
1.87
Avg. fall time
1.225
1.610
1.553
1.759
Stand. Dev.
0.068
0.043
0.042
0.055
Record the fall time, in seconds

18. Summarize Spinning Parachute Data
Depicting this data another way:
Combination
(Treatment) A
Blade width B
Blade length C
Body length
Avg. fall time
Stand. Dev.
# of Reps. 1
1.225
0.068 10 2
1.610
0.043 3
1.553
0.042 4
1.759
0.055
Grand Average
1.537

19. Analyze Results of Spinning Parachute Experiment
Calculate the effects of each of the 3 factors on the two performance characteristics
Example: Factor A, Blade width:
There are two combinations where A is at level 1
The average fall time when factor A is at level 1 is ( ) / 2 = seconds
Now consider factor A at level 2: ( ) / 2 = seconds
So the overall effect of varying Factor A between level 1 and level 2 is |1.656 – 1.418| = .238 seconds
These results also determine the level setting that leads to the longest fall time

20. Analyze Results of Spinning Parachute Experiment
Now repeat this analysis for Factors B and C A
Blade width B
Blade length C
Body length
Level Avg. Fall time
1.418
1.389
1.492
Level Avg. Fall time
1.656
1.685
1.582
Effect (difference)
0.238
0.296
0.090
Optimum level 2
Optimum configuration
wide
long

21. Representing the Results Graphically
The steepest slope between the two factor levels indicates a greater effect on the performance characteristics
1.7
1.6
1.5
1.4
1.3
Grand
average
1 2
Level
Factor A
Blade width
Level
Factor B
Blade length
Level
Factor C
Body length

22. Develop a Prediction Equation for the Best Fall Time
Blade width B
Blade length C
Body length
Level Avg. Fall time
1.418
1.389
1.492
Level Avg. Fall time
1.656
1.685
1.582
Effect (difference)
0.238
0.296
0.090
Optimum level 2
Optimum configuration
wide
long
Grand average = seconds
Max Fall Time = (1.656 – 1.537) + (1.685 – 1.537) + (1.582 – 1.537) = seconds

23. Final Step: Run a Verification Experiment
Set all factors at their optimal levels
Collect data for ten replicates
Calculate the average of the ten trials
Compare with the predicted value

24. Your Turn! With your team:
Carefully cut out four parachutes according to the four combinations from the half factorial orthogonal array
Conduct ten experiments for each of the four combinations (treatments)
Usually need to randomize the experiments, but time = limited here
Minimize the effects of other factors, such as:
Same person always drops
Perform each drop using same technique
Same position of chair (minimize air current variability)
Same person times the fall
Same cue for start and finish of fall

25. Your Turn! Continued
Collect your data: fill in the fall times for the ten x four = 40 drops
Two team members can fill in the data – preferably using the Excel spreadsheet
Perform analysis on your data
Construct your prediction equation for the longest fall time
Carefully cut one more parachute model to your recommended factor levels for the longest fall time
Run ten replicates of a verification experiment to test your prediction
Goal: within 2 standard deviations of the predicted value

26. Conclusion
I ask the teams to turn in or me their data collection and analysis form
Additional information on DOE:
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