Factor Analysis for Dissolution Time of Effervescent Tablets

1. Factor Analysis for Dissolution Time of Effervescent Tablets Niu Jinshu (2010010837) Wu Xianyu (2010010838) Cao Liuxing (2010010836) Wu Yining (2010010835) Dai Yibo (2010010833)

2. Outlines Purpose of experiment Experiment design Factors Design mythologies Experiment conduction Analytical procedure Significant factors Effects of factors 2-factor interaction 3-factor interaction Regression model Model Validation Conclusions

3. Explore how different factors affect dissolution rate Provide several implications to the dissolution process Test if the advertisement shows the correct condition Purpose of experiment

4. Fishbone diagram Experiment design – Factors (1/2)

5. Response variable • Dissolution time: 0~300s • Control variable • Volume of water • Temperature of water • Surface area of water • Tablet flavor Experiment design – Factors (2/2) • Constant variable • Composition • Place • surface area of tablets • Noise variable • Temperature around • Air pressure • Time of ups and downs of tablets

6. Design of experiments • A four-factor two-level design is employed to reveal the main effects and the interaction effects of four factors on dissolution time: • Tablet flavor (A) • Surface area of water (B) • Volume of water (C) • Temperature of water (D) • 2^4 * 2 = 32 times Design methodologies (1/3)

7. Design methodologies (2/3) Test matrix

8. Design methodologies (3/3) Factor Levels

9. Experiment conduction (1/2)

10. Snapshots Experiment conduction (2/2)

11. Analytical procedure

12. Result cubes Significant factors (1/4)

13. Significant factors (2/4) • Main effect • Surface area (B) • Not significant • Flavor (A) & Volume(C) • A little bit • Temperature(D) • quite significant

14. Significant factors (3/4)

15. Main effect • A • C • D • AD • BCD Significant factors (4/4)

16. Reduced Model

17. Flavor • Orange tablets take longer time to dissolve than peach ones Effect of factors (1/3)

18. Volume • Volume of water increases, the dissolution time becomes shorter Effect of factors (2/3)

19. Temperature • As the temperature rises, the dissolution time will be shorter Effect of factors (3/3)

20. Flavor & Temperature • The two lines are not parallel, so they have interaction Two-factor interaction

21. BCD is not quite significant • Draw the interaction plot of: • B and CD • C and BD • D and BC In order to find out BCD’s interaction Three-factor interaction (1/2)

22. Those three pairs of factors all have interaction, so BCD have significant interaction. Three-factor interaction (2/2) • C and BD • B and CD • D and BC

23. Regression model Since R-Sq is quite large, and there are only 32 observations, we do not eliminate the outlier.

24. Model validation • The evaluation results

25. Model validation • 95 significant level paired-t test

26. The main effects of flavor, volume of water and temperature of water are significant. The two-factor interactions between flavor and temperature is also significant. Surface area does not show any significant effects at either main effect or two-factor interactions. The three-factor interaction of surface area, volume of water and temperature of water is significant. 时间 = 162 - 10.2 口味 + 2.72 表面积 - 6.01 水量 - 57.7 水温 + 7.65 口味*水温- 4.28 表面积*水量*水温 The advertisement in Taobao isn’t reliable. Conclusions

27. Thanks! Q&A