Multiresponse Optimization through a Loss Function Considering Process Parameter Fluctuation

공정변수의 변동을 고려한 손실함수를 통한 다중반응표면 최적화

  • Kwon, Jun-Bum (Production Engineering Research Center, LG Electronics, Inc.) ;
  • Lee, Jong-Seok (Department of Industrial and Management Engineering, POSTECH) ;
  • Lee, Sang-Ho (Department of Industrial and Management Engineering, POSTECH) ;
  • Jun, Chi-Hyuck (Department of Industrial and Management Engineering, POSTECH) ;
  • Kim, Kwang-Jae (Department of Industrial and Management Engineering, POSTECH)
  • 권준범 (LG전자 생산기술원) ;
  • 이종석 (포항공과대학교 산업경영공학과) ;
  • 이상호 (포항공과대학교 산업경영공학과) ;
  • 전치혁 (포항공과대학교 산업경영공학과) ;
  • 김광재 (포항공과대학교 산업경영공학과)
  • Published : 2005.06.30

Abstract

A loss function approach to a multiresponse problem is considered, when process parameters are regarded as random variables. The variation of each response may be amplified through so called propagation of error (POE), which is defined as the standard deviation of the transmitted variability in the response as a function of process parameters. The forms of POE for each response and for a pair of responses are proposed and they are reflected in our loss function approach to determine the optimal condition. The proposed method is illustrated using a polymer case. The result is compared with the case where parameter fluctuation is not considered.

Keywords

References

  1. Ames, A. E., Mattucci, N., Macdonald, S., Szonyi, G. and Hawkins, D. M.(1997), Quality Loss Function for Optimization across Multiple Response Surface, Journal of Quality Technology, 29, 339-346
  2. Box, G. E. P. and Wilson, K. B.(1951), On the Experimental Attainment of Optimum Conditions, Journal of Royal Statistical Society-Series E, 13, 1-45
  3. Derringer, G. C. and Suich, R.(1980), Simultaneous Optimization of Several Response Variables, Journal of Quality Technology, 12(4), 214-219
  4. Fathi, Y.(1991), Nonlinear Programming Approach to the Parameter Design Problem, European Journal of Operational Research, 53, 371-381 https://doi.org/10.1016/0377-2217(91)90070-C
  5. Harrington, E.C.(1965), The Desirability Function, Industrial Quality Control, 4, 494-498
  6. Kim, K-J. and Lin, D.(2000), Simultaneous Optimization of Multiple Responses by Maximizing Exponential Desirability Functions, Journal of Royal Statistical Society-Series C, 43, 311-325
  7. Khuri, A. and Conlon, M.(1981), Simultaneous Optimization of Multiple Responses Represented by Polynomial Regression Functions, Technometrics, 23, 363-375 https://doi.org/10.2307/1268226
  8. Ko, Y-H., Kim, K-J. and Jun, C-H.(2005), A New Loss Function-Based Method for Multiresponse Optimization, Journal of Quality Technology, 37(1), 50-59
  9. Kwon, J-B., Lee, J-S., Lee, S-H., Jun, C-H. and Kim, K-J (2005), Multiresponse Optimization through a New Desirability Function Considering Process Parameter Fluctuation, Journal of the Korean Operations Research and Management Science Society, 30(1), 95-104
  10. Lee, M-S. and Kim, K-J.(2004), Expected Desirability Function: Consideration of Both Dispersion and Location Effects in Desirability Function Approach, Working Paper, Department of Industrial Engineering, POSTECH
  11. Myers, R. H.and Montgomery, D. C.(2002), Response Surface Methodology: Process and Product Improvement with Designed Experiments, 2nd Edition, John Wiley & Sons, New York
  12. Pignatiello, J.(1993), Strategies for Robust to Multiresponse Quality Engineering, lIE Transactions, 25, 5-15
  13. Plante, R.(2001), Process Capability: a Criterion for Optimizing Multiple Response Product and Process Design, lIE Transactions, 33, 497-509
  14. Ribeiro, J. L., E1sayed, E.A.(1995), A Case Study on Process Optimization Using the Gradient Loss Function, International Journal of Production Research, 33(12),3233-3248 https://doi.org/10.1080/00207549508904871
  15. Vining, G. G.(1998), A Compromise Approach to Multiresponse Optimization, Journalof Quality Technology, 30, 309-313