Journal of Korean Society for Quality Management (품질경영학회지)

Korean Society for Quality Management (한국품질경영학회)
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Weighted Mean Squared Error Minimization Approach to Dual Response Surface Optimization: A Process Capability Indices-Based Weighting Procedure

쌍대반응표면최적화를 위한 가중평균제곱오차 최소화법: 공정능력지수 기반의 가중치 결정

  • Jeong, In-Jun (Department of Business Administration, Daegu University)
  • Received : 2014.10.10
  • Accepted : 2014.12.12
  • Published : 2014.12.31
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Abstract

Purpose: The purpose of this paper is to develop a systematic weighting procedure based on process capability indices method applying weighted mean squared error minimization (WMSE) approach to dual response surface optimization. Methods: The proposed procedure consists of 5 steps. Step 1 is to prepare the alternative vectors. Step 2 is to rank the vectors based on process capability indices in a pairwise manner. Step 3 is to transform the pairwise rankings into the inequalities between the corresponding WMSE values. Step 4 is to obtain the weight value by calculating the inequalities. Or, step 5 is to obtain the weight value by minimizing the total violation amount, in case there is no weight value in step 4. Results: The typical 4 process capability indices, namely, $C_p$, $C_{pk}$, $C_{pm}$, $C_{pmk}$ are utilized for the proposed procedure. Conclusion: The proposed procedure can provide a weight value in WMSE based on the objective quality performance criteria, not on the decision maker's subjective judgments or experiences.

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References

  1. Box, George E. P., and Draper, Norman R. 1987. Empirical Model Building and Response Surfaces. New York:John Wiley&Sons.
  2. Chan, Lai K., Cheng, Smiley W., and Spiring, Frederick A. 1988. "A New Measure of Process Capability Cpm." Journal of Quality Technology 20(3):162-175. https://doi.org/10.1080/00224065.1988.11979102
  3. Cho, Moonsoo, and Lim, Taejin. 2002. "The Relation between the Process Capability Index and the Quality Assurance Level Considering Various Conditions." Journal of the Korean Society for Quality Management 30(2):130-151.
  4. Copeland, Karen A. F., and Nelson, Peter R. 1996. "Dual Response Optimization via Direct Function Minimization." Journal of Quality Technology 28(3):331-336. https://doi.org/10.1080/00224065.1996.11979683
  5. Ding, Rui, Lin, Dennis K. J., and Wei, Duan. 2004. "Dual Response Surface Optimization: A Weighted MSE Approach." Quality Engineering 16(3):377-385. https://doi.org/10.1081/QEN-120027940
  6. Hsiang, Thomas C., and Taguchi, Genichi. 1985. A Tutorial on Quality Control and Assurance - the Taguchi methods. ASA Annual Meeting, Las Vegas, Nevada, USA.
  7. Jeong, In-Jun, Kim, Kwang-Jae, and Chang, Soo Y. 2005. "Optimal Weighting o f Bias a nd V ariance in D ual Response Surface Optimization." Journal of Quality Technology 37(3):236-247. https://doi.org/10.1080/00224065.2005.11980324
  8. Juran, Joseph M. 1974. Quality Control Handbook, 3rd ed. New York: McGraw-Hill.
  9. Kane, Victor E. 1986. "Process Capability Indices." Journal of Quality Technology 18(1):41-52. https://doi.org/10.1080/00224065.1986.11978984
  10. Khuri, Andre I., and Cornell, John A. 1996. Response Surfaces: Designs and Analyses. New York: Dekker.
  11. Kim, K, Jun, C, Cho, H, Hong, Y, Kim, Y, Kim, C, Youm, S, Lee, S, Lee, J, Chang, B, Jeong, B, and Jeong, I. 2000. Development of a Six-Sigma Improvement Model: Reducing the Variation of Tin Plates' Hardness. Technical Report, POSCO, Republic of Korea.
  12. Kim, Kwang-Jae, and Lin, Dennis K. J. 1998. "Dual Response Surface Optimization: a Fuzzy Modeling Approach." Journal of Quality Technology 30(1):1-10. https://doi.org/10.1080/00224065.1998.11979814
  13. Kim, Young-Jin. 2002. "Response Surface Approach to Integrated Optimization Modeling for Parameter and Tolerance Design." Journal of the Korean Society for Quality Management 30(4):58-67.
  14. Ko, Young-Hyun, Kim, Kwang-Jae, and Jun, Chi-Hyuk. 2005. "A New Loss Function- Based Method for Multiresponse Optimization." Journal of Quality Technology 37(1):50-59. https://doi.org/10.1080/00224065.2005.11980300
  15. Koksoy, Onur, and Doganaksoy, Necip. 2003. "Joint Optimization of Mean and Standard Deviation Using Response Surface Methods." Journal of Quality Technology 35(3):239-252. https://doi.org/10.1080/00224065.2003.11980218
  16. Lee, Dong-Hee, and Kim, Kwang-Jae. 2012. "Interactive Weighting of Bias and Variance in Dual Response Surface Optimization." Expert Systems with Applications 39(5):5900-5906. https://doi.org/10.1016/j.eswa.2011.11.114
  17. Lee, Dong-Hee, Jeong, In-Jun, and Kim, Kwang-Jae. 2010. "A Posterior Preference Articulation Approach to Dual -Response-Surface Optimization." IIE Transactions 42(2):161-171.
  18. Lee, Kangin, and Han, Seokman. 2005. "A Case Study of Continuous Improvement Methodology by Calculatged Quality-Cost." Journal of the Korean Society for Quality Management 33(3):19-30.
  19. Lee, Sun-Ryong. 2012. Modern Quality Management, Gyeonggi: Bobmunsa.
  20. Lee, Woo-Sun, and Rheem, Sung-Sue. 2001. "Some 3-Level Spherical Designs for Response Surface Experiments:Designs Constructed for the Radius of the Spherical Experimental Region to Vary with the Number of Factors." Journal of the Korean Society for Quality Management 29(1):24-40.
  21. Lin, Dennis K. J., and Tu, Wanzhu. 1995. "Dual Response Surface Optimization." Journal of Quality Technology 27(1):34-39. https://doi.org/10.1080/00224065.1995.11979556
  22. Myers, Raymond. H., and Montgomery, Douglas. C. 2002. Response Surface Methodology, 2nd ed. New York:John Wiley&Sons.
  23. Pearn, Wen Lea, Kotz, Samuel, and Johnson, Norman L. 1992. "Distributional and Inferential Properties of Process Capability Indices." Journal of Quality Technology 24(4):216-231. https://doi.org/10.1080/00224065.1992.11979403
  24. Rheem, Sung-Sue, and Lee, Woo-Sun. 2005. "Multiresponse Optimization in Response Surface Analysis: A Method by Minimization of Weighted Sum of Estimates of Expected Squared Relative Errors." Journal of the Korean Society for Quality Management 33(1):73-82.
  25. Shin, Sangmun, and Cho, Byung Rae. 2006. "Robust Design Models for Customer-Specified Bounds on Process Parameters." Journal of Systems Science and Systems Engineering 15(1):2-18. https://doi.org/10.1007/s11518-006-0002-4
  26. Sullivan, Lawrence P. 1984. "Targeting Variability - A New Approach to Quality." Quality Progress 17(7): 15-21.
  27. Sullivan, Lawrence P. 1985. "Letters." Quality Progress 18(4):7-8.
  28. Tang, L. C., and Xu, K. 2002. "A Unified Approach for Dual Response Surface Optimization." Journal of Quality Technology 34(3):437-447. https://doi.org/10.1080/00224065.2002.11980175
  29. Vining, G. Geoffrey, and Myers, Raymond H. 1990. "Combining Taguchi and Response Surface Philosophies: A Dual Response Approach." Journal of Quality Technology 22(1):38-45. https://doi.org/10.1080/00224065.1990.11979204
  30. Yook, Keun-Hyo. 2010. "The Effect of Financial and Operational Quality Measures on Firm Financial Performance." Productivity Review 24(1):111-128. https://doi.org/10.15843/kpapr.24.1.201003.111