1. Design of Experiments (DOE) Helicopters Team Rubber Ducky Emily Kalberer, Daniel Chavez, Allison Raniere

2. Purpose of Experiment The purpose of this project is to use the DOE procedure to: ▫Write a prediction equation for the frequency using Coded Factors. ▫Predict the height of random dimensions given. ▫Understand how DOE is more efficient versus the One-Factor-at-a-time tactic.

3. Factors Blade Length (L) Fold Length (F) Low Setting: 14 cm High Setting: 28 cm Low Setting: 1 cm High Setting: 2cm

4. Our Designs Low-Low (1) Setting Low-High (b) Setting

5. High-Low (a) SettingHigh-High (ab) Setting

6. Models in action (1) Avg. Height: 1.62m(b) Avg. Height: 0.93m

7. (a) Avg. Height: 1.24m(ab) Avg. Height: 1.46m

8. Main Effects Plot L F 7cm 14cm 1cm2cm 0.931.62 1.24 1.46

9. Interaction Plot 0.5m 1.0m 1.5m 2.0m 0.93m 1.24m 1.24m (-) 1.46m (+) Shows evidence of Interaction

10. Main Effects and Interaction Effects A = ((a-(1))+(ab-b))/2L = ((1.24-1.62)+(1.46-0.93))/2 = 0.075 B = ((b-(1))+(ab-a))/2F = ((0.93-1.62)+(1.46-1.24))/2 = -0.235 AB = ((ab+(1))-(a+b))/2LF = ((1.46+1.62)-(1.24+0.93))/2 = -0.045

11. Prediction Equation Y = K 1 +K A X A +K B X B +K AB X A X B K 1 = ((1)+b+a+ab)/4K 1 = (1.62+.093+1.24+1.46)/4 = 1.3125 K A = (-(1)-b+a+ab)/4K A = (-1.62-0.93+1.24+1.46)/4 = 0.0375 K B = (-(1)+b-a+ab)/4K B = (-1.62+0.93-1.24+1.46)/4 = -0.1175 K AB = ((1)-b-a+ab)/4K AB = (1.62-0.93-1.24+1.46)/4 = 0.2275 Y = 1.3125+0.0375X A -0.1175X B +0.2275X A X B

12. Predicted Height L: 13cm X A = (2(13)-14-7)/14-7 = 0.7143 F: 1.7cm X B = (2(1.7)-2-1)/2-1 = 0.4 Y = 1.42m Actual Height: 1.68m Coding: X A = (2A-A + -A - )/A + -A -

13. Percent Error (Measured-Predicted)/Measured x 100 = Percent Error (1.68-1.42)/1.68 x 100 = 15% error

14. Factor that had the greatest effect on height: Length of blade (main effect of 0.075) Conclusion Prediction model was useful in predicting the outcome because we created a small percentage of error through the coded factors of the dimensions specifically given to us. We had several sources of error such as: using different blades, imperfect measurements/ cuts, and varying fold angles. DOE was a useful technique to create a model in this situation because it’s predicted value for the specified measurements were precise compared to the actual recorded values. Our group would change our rounding for both our predicted and measured values.