Introduction to Design of Experiments

1. UA College of Engineering Introduction to Design of Experiments Brian Cunningham Jennifer Horner 03-26-11

2. 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 Consumption Production Preliminary design Detailed design

7. cut Fold forward Fold backward attach paper clip here The Spinning Parachute Company Current best-selling model:

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. cut Fold forward Fold backward attach paper clip here The Spinning Parachute Company Preliminary research: 3 main factors impact the flight time • Blade width • Blade length • Body length Blade width 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. 2 2 1 1 cut 2 1 1 2 Fold forward Fold backward attach paper clip here 1 2 The Spinning Parachute Company The company’s engineers want to test new dimensions for the three factors: Wider blade Longer blade Longer body

13. The Spinning Parachute Company There are 23, or 8, possible configurations to examine: 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 Combinations Set 1 Set 2 Each set is called a “half factorial analysis.”

16. Orthogonal Set 1 Applied to the Spinning Parachute 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) Record the fall time, in seconds

18. Summarize Spinning Parachute Data Depicting this data another way:

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 (1.225 + 1.610) / 2 = 1.418 seconds • Now consider factor A at level 2: (1.553 + 1.759) / 2 = 1.656 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

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

22. Develop a Prediction Equation for the Best Fall Time Max Fall Time = 1.537 + (1.656 – 1.537) + (1.685 – 1.537) + (1.582 – 1.537) = 1.849 seconds Grand average = 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 email me their data collection and analysis form • Additional information on DOE: • http://www.moresteam.com/toolbox/t408.cfm • http://www.isixsigma.com/index.php?option=com_k2&view=itemlist&task=category&id=199:teaching-doe&Itemid=156 • http://www.stat.psu.edu/online/courses/stat503/01_intro/02_intro_history.htmlhttp://www.camo.com/rt/Resources/design_of_experiment.html • http://thequalityportal.com/q_know02.htm