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Design of Experiment

Design of Experiment. Group member: Li Zheran Xu Zan She Manrong Lei Chen. Content :. Motivation Literature review Design of Experiment Implementation Restrictions. Motivation .

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Design of Experiment

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  1. Design of Experiment Group member: Li Zheran Xu Zan She Manrong Lei Chen

  2. Content : • Motivation • Literature review • Design of Experiment • Implementation • Restrictions

  3. Motivation • Find out the main effect on spinning top • Design a model between the effect and the response • Help understand the work principle of spinning top

  4. Content : • Motivation • Literature review • Design of Experiment • Implementation • Restrictions

  5. Literature review • The history of spinning-top: • 明代刘侗、于奕正《帝经物略·二春场》载: “陀螺者，木制，如小空钟，中实而无柄。绕以鞭之绳，卓于地，争制其鞭……”。 • 1852年, 博科(Foucault)首先将高速旋转的刚体称为陀螺。 Clockwork gyro Wooden gyro Rotating handle gyro

  6. Literature review • The process of turning spinning-top:

  7. Literature review • The process of turning spinning-top:

  8. Content : • Motivation • Literature review • Design of Experiment • Implementation • Restrictions

  9. Design of Experiment

  10. Factor Decomposition • Response Variable: Slewing time • Control variable: • Ground surface （cement / plastic / ceramic） • Height （low / high ） • Weight （light / heavy） • Fixed variables: Force （ held constant） • Nuisance factor: • Surface homogeneous • Wind speed

  11. Factor Level Definition

  12. Preliminary Experiment Choose rotating handle gyro to do the preliminary experiment to control the fixed factor • light

  13. Control the fixed factor

  14. Control the fixed factor

  15. Content : • Motivation • Literature review • Design of Experiment • Implementation • Restrictions

  16. Implementation

  17. Implementation Full Factorial Design

  18. Data analysis • Significant effect • A: type of ground surface • C: the weight of the gyro • No significant effect • B: the height

  19. Data analysis（cont.） • No interaction effect • A and B • B and C • Significant effect • A and C • On the ceramic ground, the difference is bigger.

  20. Data analysis（cont.） • Normality assumption • Normal probability plot √ • Histogram √ • Equal variance assumption • Residual VS fitted value ╳

  21. 项 系数 系数标准误 T P 常量 19.6983 0.4626 42.58 0.000 A 1 -4.8033 0.6542 -7.34 0.000 2 -10.8533 0.6542 -16.59 0.000 B 1 -0.1850 0.4626 -0.40 0.691 C 1 4.4517 0.4626 9.62 0.000 A*B 1 1 0.0400 0.6542 0.06 0.951 2 1 0.2400 0.6542 0.37 0.715 A*C 1 1 -0.6967 0.6542 -1.06 0.292 2 1 -3.3967 0.6542 -5.19 0.000 B*C 1 1 0.3217 0.4626 0.70 0.490 A*B*C 1 1 1 -0.6067 0.6542 -0.93 0.358 2 1 1 -0.1167 0.6542 -0.18 0.859 Slewing Time 的方差分析，在检验中使用调整的 SS 来源 自由度 Seq SS Adj SS Adj MS F P A 2 7719.96 7719.96 3859.98 300.64 0.000 B 1 2.05 2.05 2.05 0.16 0.691 C 1 1189.04 1189.04 1189.04 92.61 0.000 A*B 2 2.75 2.75 1.38 0.11 0.899 A*C 2 575.56 575.56 287.78 22.41 0.000 B*C 1 6.21 6.21 6.21 0.48 0.490 A*B*C 2 18.10 18.10 9.05 0.70 0.499 误差 48 616.28 616.28 12.84 合计 59 10129.95 S = 3.58317 R-Sq = 93.92% R-Sq（调整） = 92.52%

  22. Another experiment Clockwork gyro

  23. Data analysis

  24. Data analysis

  25. 项 系数 系数标准误 T P 常量 19.2759 0.4119 46.80 0.000 A 1 -4.7976 0.5450 -8.80 0.000 2 -10.5211 0.4967 -21.18 0.000 B 1 -0.1617 0.4119 -0.39 0.696 C 1 4.5355 0.4119 11.01 0.000 A*B 1 1 0.0217 0.5450 0.04 0.968 2 1 0.2241 0.4967 0.45 0.654 A*C 1 1 -0.7190 0.5450 -1.32 0.193 2 1 -3.5094 0.4967 -7.07 0.000 B*C 1 1 0.3936 0.4119 0.96 0.344 A*B*C 1 1 1 -0.6616 0.5450 -1.21 0.231 2 1 1 -0.2219 0.4967 -0.45 0.657 Slewing Time 的方差分析，在检验中使用调整的 SS 来源 自由度 Seq SS Adj SS Adj MS F P A 2 273.476 308.292 154.146 291.91 0.000 B 1 0.089 0.081 0.081 0.15 0.696 C 1 38.019 64.031 64.031 121.26 0.000 A*B 2 0.537 0.113 0.056 0.11 0.899 A*C 2 29.137 29.028 14.514 27.49 0.000 B*C 1 0.136 0.482 0.482 0.91 0.344 A*B*C 2 0.973 0.973 0.487 0.92 0.405 误差 48 25.347 25.347 0.528 合计 59 367.714 S = 0.726677 R-Sq = 93.11% R-Sq（调整） = 91.53%

  26. The results of the design • Main effect: Ground surface & weight with 95% confidence • Ground surface effect: Ceramic material increases the slewing time • Weight effect: Lighter gyro increases the slewing time

  27. Content : • Motivation • Literature review • Design of Experiment • Implementation • Restrictions

  28. Restrictions on the experiment • Force control: Though we have practice to keep force constant, there is still personal error. • Difficult to control the weight: To control the weight, we choose to cover plasticine to plus weight. • Data acquisition: Each run we use stopwatch to record data, which may have measuring error. • Wearing restriction: With the increasing of run times, the gyro wearing increases.

  29. Thank you for listening Q&A

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