Response Surface Method in the Presence of Uncontrollable Factors

Kiani, Mehdi

doi:10.61186/jss.17.1.2

[Home ] [Archive]

[ فارسی ]

مجله علوم آماری – نشریه علمی پژوهشی انجمن آمار ایران

Main Menu

Home

Journal Information

Articles archive

For Authors

For Reviewers

Registration

Ethics Considerations

Contact us

Site Facilities

Search in website

Receive site information

Indexing and Abstracting

Social Media

Licenses

This Journal is licensed under a Creative Commons Attribution NonCommercial 4.0
International License
(CC BY-NC 4.0).

Similarity Check Systems

Volume 17, Issue 1 (9-2023)

JSS 2023, 17(1): 0-0

Back to browse issues page

Response Surface Method in the Presence of Uncontrollable Factors

Mehdi Kiani ^*

Abstract: (1594 Views)

In the 1980s, Genichi Taguchi, a Japanese quality advisor, claimed that most of the variability affiliated with the response could be attributed to the company of unmanageable (noise) factors. In some practical cases, his modeling proposition evidence leads the quality improvement to many runs in a crossed array. Hence, several researchers have em-braced noteworthy attitudes of response surface methodology along with the robust parameter design action as alternatives to Taguchi's plan. These alternatives model the response's mean and variance corresponding to the combination of control and noise factors in a combined array to accomplish a robust process or production. Indeed, using response surface methods to the robust parameter design minimises the impression of noise factors on assembling processes or productions. This paper intends to develop further modeling of the predicted response and variance in the presence of noise factors based on unbiased and robust estimators. Another goal is to design the experiments according to the optimal designs to improve these estimators' accuracy and precision simultaneously.

Keywords: Response Surface, Robust Parameter Design, Optimal Designs.

Full-Text [PDF 1049 kb] (1408 Downloads)

Type of Study: Research | Subject: Applied Statistics
Received: 2022/04/24 | Accepted: 2023/09/1 | Published: 2023/07/11

References

1. Arora, J. S. (2017). Introduction to Optimum Design. 4th Edition. Elsevier Science.

2. Borror, C. M., Montgomery, D. C., and Myers, R. H. (2002). Evaluation of statistical designs for ex-periments involving noise variables. Journal of Quality Technology. Vol. 34, pp. 54-70. [DOI:10.1080/00224065.2002.11980129]

3. Box, G. E. P. (1988). Signal-to-Noise Ratio, Performance Criteria, and Transformation. Technomet-rics, Vol. 30, pp. 1-17. [DOI:10.1080/00401706.1988.10488313]

4. Box, G. E. P., and Jones, S. (1990). Designing Products That Are Robust To The Environment. Re-port Series in Quality and Productivity. CPQI, University of Wisconsin, Number 56.

5. Box, G. E. P., and Wilson, K. B. (1951). On the Experimental Attainment of Optimum Conditions (with discussion). Journal of the Royal Statistical Society, Series B, Vol. 13, pp. 1-45. [DOI:10.1111/j.2517-6161.1951.tb00067.x]

6. Boylan, G. L., Goethals, P. L., and Cho, B. R. (2013). Robust Parameter Design in Resource-Constrained Environments: an Investigation of Trade-offs Between Vosts and Precision Within Variable Processes. Applied Mathematical Modelling. Vol. 37, pp. 2394-2416. [DOI:10.1016/j.apm.2012.05.017]

7. Chan, L. K., and Xiao, P. H. (1995). Combined Robust Design. Quality Engineering, Vol. 8, pp. 47-56. [DOI:10.1080/08982119508904604]

8. Copeland, K. A. F., and Nelson, P. R. (1996). Dual Response Optimization via Direct Function Min-imization. Journal of Quality Technology, Vol. 28, pp. 331-336. [DOI:10.1080/00224065.1996.11979683]

9. Del Castillo E., and Montgomery, D. C. (1993). A nonlinear programming solution to the dual re-sponse problem. Journal of Quality Technology, Vol. 25, pp. 199-204. [DOI:10.1080/00224065.1993.11979454]

10. Kiani, M. (2010). Extensions to Modified Gram-Schmidt Strategy and Its Application in Steepest Ascent Method. Journal of Statistical Computation and Simulation, Vol. 80, pp. 389-400. [DOI:10.1080/00949650802662813]

11. Kiani, M. (2012). On the Construction of Optimal Designs. Journal of Statistical Computation and Simulation, Vol. 82, pp. 1003-1014. [DOI:10.1080/00949655.2011.563739]

12. Lee, Y., and Nelder, J. A. (1998). Joint Modeling of Mean and Dispersion. Technometrics, Vol. 40, pp. 168-175. [DOI:10.2307/1270676]

13. Lee, Y., and Nelder, J. A. (2003). Robust Design via Generalized Linear Models. Journal of Quality Technology, Vol. 35, pp. 2-12. [DOI:10.1080/00224065.2003.11980187]

14. Li, W., and Wu, C. F. J. (1999). An Integrated Method of Parameter Design and Tolerance Design. Quality Engineering, Vol. 11, pp. 417-425. [DOI:10.1080/08982119908919258]

15. Lin, D. K. J. and Tu, W. (1995). Dual Response Surface Optimization. Journal of Quality Technolo-gy, Vol. 27, pp. 248-260. [DOI:10.1080/00224065.1995.11979556]

16. MacKay, R. J., and Steiner, S. H. (1997). Strategies for Variability Reduction. Quality Engineering, Vol. 10, pp. 125 -136. [DOI:10.1080/08982119708919115]

17. Miro-Quesada, G., and Del Castillo, E. (2004). Two Approaches for Improving the Dual Response Method in Robust Parameter Design. Journal of Quality Technology, Vol. 36, pp. 154-168. [DOI:10.1080/00224065.2004.11980262]

18. Montgomery, D. C. (2020). Design and Analysis of Experiments. 10th Edition, John Wiley & Sons, New York.

19. Myers R. H., Montgomery, D. C., and Anderson, C. M. (2016). Response Surface Methodology: Pro-cess and Product Optimization Using Designed Experiments. 4th Edition, John Wiley and Sons, New York, NY.

20. Myers R. H., Khuri A. I., and Vining G. G. (1992). Response Surface Alternatives to the Taguchi Robust Parameter Design Approach. The American Statistician, Vol. 46 pp. 131-139. [DOI:10.1080/00031305.1992.10475869]

21. Myers, R. H., Khuri, A. I., and Carter, W. H. (1989). Response Surface Methodology: 1966-1988. Technometrics, Vol. 31, pp. 137-157. https://doi.org/10.2307/1268813 [DOI:10.1080/00401706.1989.10488509]

22. Myers, W. R., Brenneman, W. A., and Myers, R. H. (2005). A Dual-Response Approach to Robust Parameter Design for a Generalized Linear Model. Journal of Quality Technology, Vol. 37, pp. 130-138. [DOI:10.1080/00224065.2005.11980311]

23. Nelder, J. A., and Lee, Y. (1991). Generalized Linear Models for the Analysis of Taguchi-Type Ex-periments. Applied Stochastic models and Data Analysis, Vol. 7, pp. 107-120. [DOI:10.1002/asm.3150070110]

24. Rodriguez, M., Montgomery, D. C., and Borror, C. M. (2009). Generating Experimental Designs In-volving Control and Noise Variables Using Genetic Algorithms. Quality and Reliability Engi-neering International, Vol. 25, pp. 1045-1065. [DOI:10.1002/qre.1020]

25. Searle, S.R., Casella, G. and McCulloch, C.E. (2006). Variance Components. John Wiley & Sons, New York, NY.

26. Shin, S., Samanlioglu, F., Cho, B. R., Wiecek, M. M. (2011). Computing Trade-offs in Robust De-sign: Perspectives of the Mean Squared Error. Computers and Industrial Engineering, Vol. 60, pp. 248-255. [DOI:10.1016/j.cie.2010.11.006]

27. Shoemaker, A. C., Tsui, K. L., and Wu, C. F. J. (1991). Economical Experimentation Methods for Robust Design. Technometrics, Vol. 33, pp. 415-427. [DOI:10.1080/00401706.1991.10484870]

28. Taguchi, G. (1986). Introduction to Quality Engineering. Tokyo, Japan: Asian Productivity Organiza-tion.

29. Taguchi, G. (1987). System of Experimental Design: Engineering Methods to Optimize Quality and Minimize Cost. Quality Resources, White Plains, NJ.

30. Vining, G. C., and Myers, R. H. (1990). Combining Taguchi and response surface philosophies: a dual response approach. Journal of Quality Technology, Vol. 22, pp. 38-45. [DOI:10.1080/00224065.1990.11979204]

31. Welch, W. J., Yu, T. K., Kang, S. M., and Sacks, J. (1990). Computer Experiments for Quality Con-trol by Parameter Design. Journal of Quality Technology, Vol. 22, pp. 15-22. [DOI:10.1080/00224065.1990.11979201]

32. Wu, C. F. J., and Hamada, M. (2021). Experiments: Planning, Analysis, and Parameter Design Opti-mization. 3rd Edition. John Wiley & Sons, New York. [DOI:10.1002/9781119470007]

33. Wu, C. F. J., and Zhu, Y. (2003). Optimal Selection of Single Arrays for Parameter Design Experi-ments. Statistica Sinica, Vol. 13, pp. 1179-1199.

Send email to the article author

Add your comments about this article