1. GROUP ASSIGNMENT REPORT Group One Chen Yongtao Kuang Yun Zhu Zhenxuan Wang Gaonan Cheng Yuchen 2010.6.6

2. AGENDA 1. Abstract 2. Structure of the Catapult 3. The Fish-bone Diagram 4. Design of the Experiment 5. Analysis of the Experimental Data 6. Optimization 7. Test of the Results and Conclusion 8. Weakness and Possible Improvement 9. References

3. ABSTRACT A study on the factors that influence the ejection range of the catapult Topic: Elucidate the influence of the factors and try to find the best combination of the parameters which make the ejection range closest to 2.7 m Goal: We found 3 combinations of the parameters and chose the best combination with std.=6.4 Experimental Result:

4. STRUCTURE OF THE CATAPULT A 是橡皮筋支点的位置，有 4 个 level B 是挡板的位置，有 6 个 level C 是投石杆发射的位置，是个连续变量

5. The fish-bone diagram

6. DESIGN OF THE EXPERIMENT (1) Detail of variables: 控制变量 （单位） control variable (units) 正常水平与 可操作范围 normal level & range 测量精度 与方法 meas. precision & setting error How known? 推荐试验设置 proposed settings, based on predicted effects 对响应变量的 预期效果 predicted effects (for various responses) 橡皮筋支点 水平 4 个位 置 标号记录 1 号位置，此时弹力最大支点越高，飞得 越远 挡杆的位置 依次 6 个位 置 标号记录投石杆与挡杆水平位置越 接近越好，但投石杆不得 超过挡杆 挡杆位置越靠 前，球飞得越远 投石杆发射的 位置 ( 角度 ) 120—180° 刻度记录 精度： 0.1° 投石杆与挡杆水平位置越 接近越好，但投石杆不得 超过挡杆 投石杆发射位置 越接近水平位置， 发射距离越远

7. DESIGN OF THE EXPERIMENT (2) Detail of fixed variables: 固定变量（单位） factor (units) 期望试验设置值 及允许变动范围 desired experimental level & allowable range 测量精度与方法 measurement precision How known? 变量控制方法 how to control (in experiment) 预期效果 anticipated effects 水平仪（手机自 带） 使用胶带固定 实验过程中车身 一直保持水平 直尺圆规 用力方向控制 弹球飞出方向平 行于车身的朝向 固定张力橡皮筋 （ N/cm ） 使用一根 无 不要将橡皮筋弄 裂或弄断 一直使用一根橡 皮筋 弹球质量（ g ）弹球质量差别小 于平均质量的 5% 电子秤剔除质量过重或 者过轻的弹球 弹球质量基本均 等

8. DESIGN OF THE EXPERIMENT (3) Parameters. 干扰参数（单位） nuisance factor (units) 测量精度及方法 measurement precision How known? 试验应对策略 strategy (e.g., randomization, blocking, etc.) 预期效果 anticipated effects 试验地风速（ m/s ） 风速计 / 人体感觉 尽量在室内、空 气流速慢的地段进 行试验 避免风速对弹球的飞 行距离造成影响 测距卷尺位移（ cm ）另一个卷尺测量 固定卷尺起点于 地面 避免试验过程中卷尺 的位移

9. DESIGN OF THE EXPERIMENT (4)

10. ANALYSIS OF THE EXPERIMENTAL DATA (1) Here are the data: Our response values are Mean and std. So totally we have 8 data.

11. ANALYSIS OF THE EXPERIMENTAL DATA (2) Main effects chart and interaction chart of Mean distance:

12. ANALYSIS OF THE EXPERIMENTAL DATA (3) Main effects chart and interaction chart of std.:

13. ANALYSIS OF THE EXPERIMENTAL DATA （ 2 ） For mean distance: We can obtain the following model ：

14. ANALYSIS OF THE EXPERIMENTAL DATA （ 3 ） For standard deviation: The model of std.:

15. OPTIMIZATION(1) As our goal is set the range closest to 2.7m and get the smallest std., we define our strategy as “setting one parameter to make the std. as small as possible, then adjust the other two parameters to get mean of 2.7m”. Solution 1: According to the main effect chart, we should set C to be -1, that is x3=150°.

16. OPTIMIZATION(2) We can see that the range never reaches 2.7m when C take the smallest value, so we should adjust A and B and try to find a combination. Solution 1 is A=1,B=5,C=158°. Set mean with 270, then To make x3 small, we can set x1=-1 and x2=1.

17. OPTIMIZATION(3) Solution 2: We set A with the largest value, then follow the previous steps. Solution 2 is A=4,B=3,C=176.4°.

18. OPTIMIZATION(4) Solution 3: We set B with the smallest value, then follow the previous steps: Solution 3 is A=3,B=2,C=171°.

19. TEST OF THE RESULTS AND CONCLUSION(1) Test of solution 1 Using the model, we can obtain: Mean distance=288.6cm, std.=12.74cm Then we got 12 distances under this experimental condition, and here is the histogram of these data:

20. TEST OF THE RESULTS AND CONCLUSION(2) Test of solution 2 Using the model, we can obtain: Mean distance=270.9cm, std.=7.98cm Then we got 10 distances under this experimental condition, and here is the histogram of these data:

21. TEST OF THE RESULTS AND CONCLUSION(3) Test of solution 3 Using the model, we can obtain: Mean distance=275.7cm, std.=7.29cm Then we got 10 distances under this experimental condition, and here is the histogram of these data:

22. TEST OF THE RESULTS AND CONCLUSION(4) Conclusion After compared the performance of the above three solutions, we can see the best solution is solution 2——A=4, B=3, C=176.4°

23. WEAKNESS AND POSSIBLE IMPROVEMENTS We didn’t consider the second-order relationship in the model. In our analysis, we treat the mean and std. of a five-value group as the response variables, so we only have 8 response values, and we have no replications. As a result, the model we obtained has relatively large error.

24. References Design and Analysis of Experiments(Sixth Edition), Douglas C.Montgomery, 2005

25. THANK YOU!

26. Q&A