Group Assignment Report

1. Group Assignment Report Group One Chen YongtaoKuang Yun Zhu Zhenxuan Wang Gaonan Cheng Yuchen 2010.6.6

2. AGENDA • Abstract • Structure of the Catapult • The Fish-bone Diagram • Designof the Experiment • Analysis of the Experimental Data • Optimization • Test of the Results and Conclusion • Weakness and Possible Improvement • References

3. ABSTRACT

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. DESIGNOF THE EXPERIMENT (1) • Detail of variables:

7. DESIGNOF THE EXPERIMENT (2) • Detail of fixed variables:

8. DESIGNOF THE EXPERIMENT (3) • Parameters.

9. DESIGNOF THE EXPERIMENT (4) • Take two levels of A, B and C, we denote: • A: The hole at the highest level is -1, and the lowest be +1. • B: The second hole is -1, and the fifth one is +1. • C: Make ，andas +1. • Then we conduct a full factorial design. • There are 8 combinations of parameters, each of which we do 5 replications, and totally we get 40 groups of data.

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. Set mean with 270, then To make x3 small, we can set x1=-1 and x2=1. Solution 1 is A=1,B=5,C=158°.

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