A Study on Battery Working Time of Laptop Computers

1. A Study on Battery Working Time of Laptop Computers Li Yangfan Liu Xiaomin Wang Chenchen Xu xu Zhang Sicheng 2009.06.08

2. Agenda

3. 1 Background

4. Background • We use laptops every day. • When the school turns off the power, we have to use the battery as the electrical source. • How long can the battery support our laptop in different cases? • How can we steadily prolong the time?

5. 2 Objective

6. Objective • To develop a statistically reliable analysis of possible factors that may have influence on the battery working time of laptops while listening to music. • To give suggestions to us students to prolong battery working time and at the same time achieve robustness.

7. 3 Factors

8. Former Research • In 2005, experts from Dell Corp. studied the power consumed when running a particular workload. • They also compared the expected battery life under different brightness levels.

9. Factors Related To Battery Working Time Response Variable!

10. Factors in Our Project • Controllable factors: • Screen brightness • Volume • Download or online • Battery using scheme • Uncontrollable factors (Noise factors): • Temperature • Frequency of pauses • Signal factor • Time

11. Levels of Controllable Factors • Screen brightness • Low: the minimum brightness that one can tolerate • High: the maximum brightness of the laptop computer • Volume • Low: the comfortable volume in earphones • High: the maximum volume of the laptop computer • Download or online • Low: listen to music after download (in TTPlayer) • High: listen to music online (in GoogleMusic) • Battery use scheme • Low: maximum battery life (最大电池模式) • High: power source optimized (最小电源模式)

12. Levels of Noise Factors • Battery temperature • Low: with radiator (散热器)open, room temperature • High: without radiator, high temperature • Frequency of pauses • Low: no pauses • High: 120s play – 30s pause

13. Level of Signal Factor -- Time • Significant • Not too short • Economic • Not too long • 5 levels • 0, 5, 10, 15, 20

14. 4 Design

15. Design of Experiment • Orthogonal Array (Taguchi) Design • 4 controllable factors • 2 noise factors • Dynamic Taguchi Design • 1 signal factor • Dynamic Taguchi Design with 32 runs • Estimation of 8 (4*2) controllable-noise interactions

16. 5 Analysis

17. Data Analysis • Four things under interest • S/N Ratio • Slope • Standard Deviation • Response-Signal Relationship

18. S/N Ratio • Qualitative Exploration • Quantitative Confirmation • Model Fitting • S/N Ratio = 8.31 + 1.13 Brightness + 1.28 Volume + 0.926 Online - 0.830 Scheme • Residual Checking • Conclusion • Volume High, Brightness High, Online High, Scheme Low

19. Slope • Qualitative Exploration • Quantitative Confirmation • Model Fitting • Slope = 0.816 + 0.0608 Brightness + 0.111 Volume + 0.0546 Online - 0.131 Scheme + 0.0588 Temperature – 0.0392 Online * Temperature • Residual Checking • Conclusion • Scheme High, Volume Low, Brightness Low, Online Low

20. Standard Deviation • Qualitative Exploration • Quantitative Confirmation • Model Fitting • LSTD = -1.17 + 0.0524 Temperature - 0.0535 Scheme - 0.0273 Pauses + 0.0537 Scheme * Pauses • Residual Checking (Natural Log Transformation) • Conclusion • Scheme High, Brightness High, Online High, Volume High

21. Response-Signal Relationship • Qualitative Exploration • Quantitative Confirmation Source DF SS F P Linear 1 5313.80 725.04 0.000 Quadratic 1 0.14 0.02 0.889 Cubic 1 0.03 0.00 0.951

22. 6 Optimization

23. Contradictions Exist… • From response table: • How to balance these goals and make trade-offs?

24. Heuristic Method • Rank first • Volume High, Scheme High, Brightness High, Online High • S/N Ratio = 10.82 • Slope= 0.9114 • LSTD = -1.224 • Standard Deviation = 0.123 • 18.228% battery power per 20 min • Battery working time = 109.7 min • Not a satisfying result

25. Optimal Method – A Possible Way • Take advantage of linear models • Change into a mixed Integer Programming problem • Something that should be paid attention to • Brightness and Volume are quantitative (-1 ~ ~1) • Online and Scheme are qualitative (-1 or 1) • LINGO Program • Maximize S/N Ratio or Minimize Standard Deviation • Subject to Slope no more than a tolerance level (0.5)

26. Optimal Method – Program

27. Optimal Method – Program

28. Optimal Method -- Example • Maximize S/N Ratio • Subject to Slope no more than 0.5 • S/N Ratio = 4.911 • Slope = 0.5 • LSTD = -1.224 • Standard Deviation = 0.123 • Brightness = -0.32 • Volume = -1 • Online = -1 • Scheme = 1 • 10% battery power per 20 min • Battery working time = 200 min

29. 7 Conclusion

30. Individual Local Optimum

31. Global Optimum • Depends on how you combine the three different goals • General recommendations:

32. 8 Discussion

33. About RPD Problem • Robust Parameter Design optimizes multiple goals • Balance different goals in an acceptable way • Huge amount of ways… • Objective function or Constraint • Combination or Separation • Our way is among them

34. 9 References

35. References • CHAPTER 10_OA&RSM.pdf, Kaibo Wang • MINITAB HELP, Minitab Inc. • DESIGN AND ANALYSIS OF EXPERIMENTS, Douglas C. Montgomory • CHINESE ELECTRONICS DAILY (Aug 16, 2005) • WHITE PAPER (Apr 2005), Dell Corporation • LAPTOP BATTERY, • http://baike.baidu.com/view/30300.htm • SEVERAL FACTORS AFFECTING BATTERY LIFETIME, http://support1.ap.dell.com/cn/zh/forum/thread.asp?fid=25&tid=36917

36. Q&A Thank you!