Design of Experiments

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Design of Experiments

• Catapult Example

Matthew Wick
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What is DOE?

• Def. - The use of structured, experimental
  methods to determine the relationships between
  different factors that affect the outcome of a
  process

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History of DOE

• Developed by Sir Ronald A. Fisher
• gt Renowned mathematician and geneticist
• gt Introduced in early 1920s

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What does DOE involve?

• Design a set of 10-20 experiments where any
  important factors are systematically varied two
  or more at a time
• Analyze the experimental results to help identify
  
• a. Any optimal conditions
• b. Factors which strongly influence test
  results
• c. Factors which do not influence test results
• d. The existence of any interactions between
  factors

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Important Side-note!

• All tests MUST be run in a random order so as to
  avoid any bias in the experimental results !

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Advantages of DOE

• Only have to test at the high (1) and low (-1)
  values for any particular experimental factor
• gt Can skip testing the increments between highs
  and lows
• gt Greatly reduces the number of experiments
  needed for accurate results
• -This saves Time, Money, Resources, and Effort

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Advantages of DOE

• Can test more than one factor at a time
• gt Allows judgment on the significance of input
  factors ..
• a. Acting alone on the output
• And
• b. Interacting with one another
• on the output

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DOE using Catapult example

• Randomly ran tests on distance of a catapults
  trajectory
• Three variables identified which may or may not
  affect distance
• 1. Launch arm height
• 2. Base stopping point
• 3. Front bracket height

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DOE using Catapult example

• The three variables are studied at their high
  (1) and low (-1) levels
• 1. Launch arm height (in.)
• gtLow 7 , High 12
• 2. Base stopping point (in.)
• gtLow 3 , High 6
• 3. Front bracket height (in.)
• gtLow 5 , High 9

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DOE using Catapult example

• There were 16 tests which needed to be run to
  test all three variables
• gt 23 8 different combinations of variables at
  their high and low levels
• gt x2 16 total tests
• -because each test must be run twice in random
  order to decrease experimental error

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DOE using Catapult example

• The experimental data is statistically analyzed
  for direct single variable effects as well as
  double and triple interactions and effects

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Test Factors and Response
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Test Design Space(Tested All Combinations of
Three Factors)
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Test Plan (Tested in Random Order)
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Average Results of Two Trials for Each Experiment
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Calculate Effect of Single Factor
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Calculate Effect of Single and Interaction Factors
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Calculations to Determine Which Factors are
Significant
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Which Factors are Significant?And Mathematical
Model
Predictive Model (Note Coefficient is
half of effect) Distance 51.1 10.7A 18.3B
27.1C 2.4AB 4.6BC
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Contour Plot of Results Predict Distance to
Target
Example Set Launch Arm (A) at 10. To hit a
target at 70 units of distance, set B at 5 and C
at 8.
To hit a target at 30 units of distance, set B at
4 and C at 6
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Conclusion

• DOE is a strong statistical method for solving
  problems using a limited amount of experiments
• Simple systems, such as a catapult, can be used
  to model the analytic methods of DOE
• DOE is important to science because it can be
  used to create new ways of testing ideas and
  solving problems in a very efficient manner

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Reference Material

• Statistics for Experimenters, by Box, Hunter, and
  Hunter 1978
• Quality By Experimental Design, by Thomas B.
  Barker 1985
• Design and Analysis of Experiments, by Douglas C.
  Montgomery 1991
• An Introduction to Design of Experiments, by
  Larry B. Barrentine 1999