Knowledge Management Research (지식경영연구)

The Knowledge Management Society of Korea (한국지식경영학회)
권호 표지
DOI QR코드

DOI QR Code

A Univariate Loss Function Approach to Multiple Response Surface Optimization: An Interactive Procedure-Based Weight Determination

다중반응표면 최적화를 위한 단변량 손실함수법: 대화식 절차 기반의 가중치 결정

  • Received : 2019.12.23
  • Accepted : 2020.01.29
  • Published : 2020.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

Response surface methodology (RSM) empirically studies the relationship between a response variable and input variables in the product or process development phase. The ultimate goal of RSM is to find an optimal condition of the input variables that optimizes (maximizes or minimizes) the response variable. RSM can be seen as a knowledge management tool in terms of creating and utilizing data, information, and knowledge about a product production and service operations. In the field of product or process development, most real-world problems often involve a simultaneous consideration of multiple response variables. This is called a multiple response surface (MRS) problem. Various approaches have been proposed for MRS optimization, which can be classified into loss function approach, priority-based approach, desirability function approach, process capability approach, and probability-based approach. In particular, the loss function approach is divided into univariate and multivariate approaches at large. This paper focuses on the univariate approach. The univariate approach first obtains the mean square error (MSE) for individual response variables. Then, it aggregates the MSE's into a single objective function. It is common to employ the weighted sum or the Tchebycheff metric for aggregation. Finally, it finds an optimal condition of the input variables that minimizes the objective function. When aggregating, the relative weights on the MSE's should be taken into account. However, there are few studies on how to determine the weights systematically. In this study, we propose an interactive procedure to determine the weights through considering a decision maker's preference. The proposed method is illustrated by the 'colloidal gas aphrons' problem, which is a typical MRS problem. We also discuss the extension of the proposed method to the weighted MSE (WMSE).

Keywords

References

  1. 임성수, 이우선 2004. "반응표면분석에서의 다반응 최적화: 기대 상대오차제곱 추정치 가중합의 최소화에 의한 방법," 품질경영학회지 (33:1), pp. 73-82.
  2. 정인준 2011. "다중반응표면최적화: 현황 및 향후 연구방향," 품질경영학회지 (39:3), pp. 377-390. https://doi.org/10.7469/JKSQM.2011.39.3.377
  3. 정인준 2015a. "Tchebycheff Metric 기반 가중평균제곱오차 최소화법을 활용한 다중반응표면 최적화," 한국산학기술학회논문지 (16:1), pp. 97-105. https://doi.org/10.5762/KAIS.2015.16.1.97
  4. 정인준 2015b. "다중반응표면 최적화에서 가중평균제곱오차 최소화법을 위한 선호도사후제시법," 한국산학기술학회논문지 (16:10), pp. 7061-7070. https://doi.org/10.5762/KAIS.2015.16.10.7061
  5. 정인준 2017. "대화식 절차를 활용한 공정능력지수 기반 다중반응표면 최적화," 품질경영학회지 (45:2), pp. 191-208. https://doi.org/10.7469/JKSQM.2017.45.2.191
  6. 정인준 2018. "쌍대반응표면최적화를 위한 사후선호도반영법: TOPSIS를 활용한 최고선호해 선택," 지식경영연구 (19:2), pp. 151-162. https://doi.org/10.15813/kmr.2018.19.2.008
  7. 정인준 2019. "다중반응표면최적화를 위한 공정능력함수법에서 최소치최대화 기준의 활용에 관한 연구," 지식경영연구 (20:3), pp. 39-47. https://doi.org/10.15813/kmr.2019.20.3.003
  8. 정인준, 조현우 2013. "다중반응표면 최적화를 위한 가중평균제곱오차," 한국산학기술학회논문지 (14:2), pp. 625-633. https://doi.org/10.5762/KAIS.2013.14.2.625
  9. 표인수, 이재광 2016. "QFD를 이용한 기업 법무 서비스 품질 측정 및 개선에 관한 연구," 지식경영연구 (17:2), pp. 1-26. https://doi.org/10.15813/kmr.2016.17.2.001
  10. Ames, A. E., Mattucci, N., MacDonald, S., Szonyi, G., and Hawkins, D. M. 1997. "Quality Loss Functions for Optimization Across Multiple Response Surfaces," Journal of Quality Technology (29:3), pp. 339-346. https://doi.org/10.1080/00224065.1997.11979775
  11. Ardakani, M. K. and Wulff, S. S. 2013. "An Overview of Optimization Formulations for Multiresponse Surface Problems," Quality and Reliability Engineering International (29:1), pp. 3-16. https://doi.org/10.1002/qre.1288
  12. Box, G. E. P. and Draper, N. R. 1987. Empirical Model Building and Response Surfaces, New York:John Wiley & Sons.
  13. Ding, R., Lin, D. K. J., and Wei, D. 2004. "Dual Response Surface Optimization: A Weighted MSE Approach," Quality Engineering (16:3), pp. 377-385. https://doi.org/10.1081/QEN-120027940
  14. Hwang, C., Masud, A. S. M., Paidy., S. R., and Yoon, K. 1979. Multiple Objective Decision Making. Methods and Applications (Lecture Notes in Economics and Mathematical Systems), Berlin:Springer-Verlag.
  15. Jauregi, P., Gilmour, S., and Varley, J., 1997. "Characterisation of Colloidal Gas Aphrons for Subsequent Use for Protein Recovery," Chemical Engineering Journal (65:1), pp. 1-11. https://doi.org/10.1016/S1385-8947(96)03154-3
  16. Jeong, I. and Kim, K. 2003. "Interactive Desirability Function Approach to Multi-Response Surface Optimization," International Journal of Reliability, Quality and Safety Engineering (10:2), pp. 205-217. https://doi.org/10.1142/S0218539303001093
  17. Jeong, I. and Kim, K. 2005. "D-STEM: A Modified Step Method with Desirability Function Concept," Computers and Operations Research (32:12), pp. 3175-3190. https://doi.org/10.1016/j.cor.2004.05.006
  18. Jeong, I. and Kim, K. 2009. "An Interactive Desirability Function Method to Multiresponse Optimization," European Journal of Operational Research (195:2), pp. 412-426. https://doi.org/10.1016/j.ejor.2008.02.018
  19. Jeong, I., Kim, K., and Chang, S. Y. 2005. "Optimal Weighting of Bias and Variance in Dual Response Surface Optimization," Journal of Quality Technology (37:3), pp. 236-247. https://doi.org/10.1080/00224065.2005.11980324
  20. Jeong, I., Kim, K., and Lin, D. 2010., "Bayesian Analysis for Weighted Mean Squared Error in Dual Response Surface Optimization," Quality and Reliability Engineering International (26:5), pp. 417-430. https://doi.org/10.1002/qre.1058
  21. Khuri, A. I. 1996. "Multiresponse Surface Methodology," Handbook of Statistics: Design and Analysis of Experiment (Vol. 13) (eds. A. Ghosh and C. R. Rao), pp. 377-406.
  22. Kim, K. and Lin, D. 2006. "Optimization of Multiple Responses Considering Both Location and Dispersion Effects," European Journal of Operational Research (169:1), pp. 133-145. https://doi.org/10.1016/j.ejor.2004.06.020
  23. Ko, Y., Kim, K., and Jun, C. 2005. "A New Loss Function-Based Method for Multiresponse Optimization," Journal of Quality Technology (37:1), pp. 50-59. https://doi.org/10.1080/00224065.2005.11980300
  24. Koksoy, O. and Yalcinoz, T. 2006. "Mean Square Error Criteria to Multiresponse Process Optimization by a New Genetic Algorithm," Applied Mathematics and Computation (175:2), pp. 1657-1674. https://doi.org/10.1016/j.amc.2005.09.011
  25. Koksoy, O. 2008. "A Nonlinear Programming Solution to Robust Multi-Response Quality Problem," Applied Mathematics and Computation (196:2), pp. 603-612. https://doi.org/10.1016/j.amc.2007.06.023
  26. Koksoy, O. 2006. "Multiresponse Robust Design: Mean Square Error (MSE) Criterion," Applied Mathematics and Computation (175:2), pp. 1716-1729. https://doi.org/10.1016/j.amc.2005.09.016
  27. Lee, D. and Kim, K. 2012. "Interactive Weighting of Bias and Variance in Dual Response Surface Optimization," Expert Systems with Applications (39:5), pp. 5900-5906. https://doi.org/10.1016/j.eswa.2011.11.114
  28. Lijuan, S., Yu, Z., and Jun, Y. 2010. "Mean Square Error Criteria to Multiple Quality Characteristics Robust Design by the Weighted Tchebycheff Method," Advanced Materials Research (118-120), pp. 881-885.
  29. Lin, D. and Tu, W. 1995. "Dual Response Surface Optimization," Journal of Quality Technology (27:1), pp. 34-39. https://doi.org/10.1080/00224065.1995.11979556
  30. Miettinen, K. 2001. "Some Methods for Nonlinear Multi-Objective Optimization," Lecture Notes in Computer Science (1993), pp. 1-20.
  31. Myers, R. H. and Montgomery, D. C. 2002. Response Surface Methodology (2nd ed.), New York:John Wiley & Sons.
  32. Myers, R. H., Khuri, A., and Carter, W. H., Jr. 1989. "Response Surface Methodology: 1966-1988," Technometrics (31:2), pp. 137-157. https://doi.org/10.1080/00401706.1989.10488509
  33. Myers, R. H. 1999. "Response Surface Methodology: Current Status and Future Directions," Journal of Quality Technology (31:1), pp. 30-44. https://doi.org/10.1080/00224065.1999.11979891
  34. Myers, R. H., Montgomery, D. C., Vining, G. G., Borror, C. M., and Kowalski, S. M. 2004. "Response Surface Methodology: A Retrospective and Literature Survey," Journal of Quality Technology (36:1), pp. 53-77. https://doi.org/10.1080/00224065.2004.11980252
  35. Pignatiello, J. 1993. "Strategies for Robust Multiresponse Quality Engineering," IIE Transactions (25:3), pp. 5-15. https://doi.org/10.1080/07408179308964286
  36. Shin, S., Samanlioglu, F., Cho, B. B., and Wiecek, M. M. 2001. "Computing Trade-Offs in Robust Design: Perspectives of the Mean Squared Error," Computers and Industrial Engineering (60:2), pp. 248-255. https://doi.org/10.1016/j.cie.2010.11.006
  37. Steuer, R. E. 1986. Multiple Criteria Optimization: Theory, Computation, and Application, New York:John Wiley & Sons.
  38. Taguchi, G. and Wu, Y. 1979. "Off-line Quality Control," Central Japan Quality Control Association (available from American Supplier Institute, Dearborn, MI).
  39. Vining, G. 1998. "A Compromise Approach to Multiresponse Optimization," Journal of Quality Technology (30:4), pp. 309-313. https://doi.org/10.1080/00224065.1998.11979867