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Year 2017, Volume: 01 Issue: 2, 40 - 45, 29.12.2017

Abstract

References

  • G.E.P. Box and K.B. Wilson, On the Experimental Attainment of Optimum Conditions, J. Roy. Statist. Soc. Ser. B Metho. 13 (1951) 1-45.
  • G.G. Vining and R.H. Myers, Combining Taguchi and Response Surface Philosophies: A Dual Response Approach, J. Qual. Technol. 22 (1990) 38-45.
  • E. Del Castillo and D.C. Montgomery, A Nonlinear Programming Solution to the Dual Response Problem, J. Qual. Technol. 25 (1993) 199-204.
  • D.K.J. Lin and W. Tu, Dual Response Surface Optimization, J. Qual. Technol. 27 (1995) 34-39.
  • K. Kim and D.K.J. Lin, Dual Response Surface Optimization: A Fuzzy Modeling Approach, J. Qual. Technol. 30 (1998) 1-10.
  • A.C. Shoemaker, K.L, Tsui, and C.F.J. Wu, Economical Experimentation Methods for Robust Parameter Design, Technometrics. 33 (1991) 415-427.
  • K.A. Copeland and P.R. Nelson, Dual Response Optimization via Direct Function Minimization, J. Qual. Technol. 28 (1996) 331-336.
  • J.M. Lucas, How to Achieve a Robust Process Using Response Surface Methodology, J. Qual. Technol. 26 (1994). 248-260.
  • O. Köksoy and N. Doganaksoy, Joint Optimization of Mean and Standard Deviation in Response Surface Experimentation, J. Qual. Technol. 35 (2003) 239-252.
  • O. Köksoy, Multiresponse Robust Design: Mean Square Error (MSE criterion), Appl. Math. Comput. 175 (2006) 1716-1729.
  • D.C. Drain and A.M. Gough, Applications of the Upside-down Normal Loss Function, IEEE T. Semıconduct M. 9 (1996) 143–145.
  • O. Köksoy and S.S. Fan, An Upside-down Normal Loss Function-based Method for Quality Improvement, Eng. Optimiz. 44 (2012) 935-945.
  • M. Zeybek and O. Köksoy, Optimization of Correlated Multi-response Quality Engineering by the Upside-down Normal Loss Function, Eng. Optimiz. 48 (2016) 1419-1431.
  • H.J. Zimmermann, Fuzzy Sets, Decision Making, and Expert Systems, Kluwer Academic Publishers, Boston, M.A. (1987).
  • C.W. Kirkwood, Strategic Decision Making, Duxbury Press, Belmont, C.A. (1996).
  • H. Moskowitz and K. Kim, On Assessing the H Value in Fuzzy Linear Regression, Fuzzy Sets Syst. 58 (1993) 303-327.
  • G.E.P. Box and N.R. Draper, Empirical Model Building and Response Surfaces, John&Sons, New York, N.Y. (1987).

A Fuzzy Modelling Approach to Robust Design via Loss Functions

Year 2017, Volume: 01 Issue: 2, 40 - 45, 29.12.2017

Abstract

Especially in a world where
industrial development is reinforced by globalization tendencies, competitive
companies know that satisfying customers' needs and running a successful
operation requires a process that is reliable, predictable and robust.
Therefore, many of quality improvement techniques focus on reducing process
variation in line with the “loss to society” concept. The upside-down normal
loss function is a weighted loss function that has the ability to evaluate
losses with a more reasonable risk assessment. In this study, we introduce a
fuzzy modelling approach based on expected upside-down normal loss function
where the mean and standard deviation responses are fitted by response surface
models. The proposed method aims to identify a set of operating conditions to
maximize the degree of satisfaction with respect to the expected loss.
Additionally, the proposed approach provides a more informative and realistic
approach for comparing competing sets of conditions depending upon how much
better or worse a process is. We demonstrate the proposed approach in a
well-known design of experiment by comparing it with existing methods.

References

  • G.E.P. Box and K.B. Wilson, On the Experimental Attainment of Optimum Conditions, J. Roy. Statist. Soc. Ser. B Metho. 13 (1951) 1-45.
  • G.G. Vining and R.H. Myers, Combining Taguchi and Response Surface Philosophies: A Dual Response Approach, J. Qual. Technol. 22 (1990) 38-45.
  • E. Del Castillo and D.C. Montgomery, A Nonlinear Programming Solution to the Dual Response Problem, J. Qual. Technol. 25 (1993) 199-204.
  • D.K.J. Lin and W. Tu, Dual Response Surface Optimization, J. Qual. Technol. 27 (1995) 34-39.
  • K. Kim and D.K.J. Lin, Dual Response Surface Optimization: A Fuzzy Modeling Approach, J. Qual. Technol. 30 (1998) 1-10.
  • A.C. Shoemaker, K.L, Tsui, and C.F.J. Wu, Economical Experimentation Methods for Robust Parameter Design, Technometrics. 33 (1991) 415-427.
  • K.A. Copeland and P.R. Nelson, Dual Response Optimization via Direct Function Minimization, J. Qual. Technol. 28 (1996) 331-336.
  • J.M. Lucas, How to Achieve a Robust Process Using Response Surface Methodology, J. Qual. Technol. 26 (1994). 248-260.
  • O. Köksoy and N. Doganaksoy, Joint Optimization of Mean and Standard Deviation in Response Surface Experimentation, J. Qual. Technol. 35 (2003) 239-252.
  • O. Köksoy, Multiresponse Robust Design: Mean Square Error (MSE criterion), Appl. Math. Comput. 175 (2006) 1716-1729.
  • D.C. Drain and A.M. Gough, Applications of the Upside-down Normal Loss Function, IEEE T. Semıconduct M. 9 (1996) 143–145.
  • O. Köksoy and S.S. Fan, An Upside-down Normal Loss Function-based Method for Quality Improvement, Eng. Optimiz. 44 (2012) 935-945.
  • M. Zeybek and O. Köksoy, Optimization of Correlated Multi-response Quality Engineering by the Upside-down Normal Loss Function, Eng. Optimiz. 48 (2016) 1419-1431.
  • H.J. Zimmermann, Fuzzy Sets, Decision Making, and Expert Systems, Kluwer Academic Publishers, Boston, M.A. (1987).
  • C.W. Kirkwood, Strategic Decision Making, Duxbury Press, Belmont, C.A. (1996).
  • H. Moskowitz and K. Kim, On Assessing the H Value in Fuzzy Linear Regression, Fuzzy Sets Syst. 58 (1993) 303-327.
  • G.E.P. Box and N.R. Draper, Empirical Model Building and Response Surfaces, John&Sons, New York, N.Y. (1987).
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Melis Zeybek

Onur Köksoy

Publication Date December 29, 2017
Submission Date September 27, 2017
Acceptance Date December 25, 2017
Published in Issue Year 2017 Volume: 01 Issue: 2

Cite

APA Zeybek, M., & Köksoy, O. (2017). A Fuzzy Modelling Approach to Robust Design via Loss Functions. Turkish Journal of Forecasting, 01(2), 40-45.
AMA Zeybek M, Köksoy O. A Fuzzy Modelling Approach to Robust Design via Loss Functions. TJF. December 2017;01(2):40-45.
Chicago Zeybek, Melis, and Onur Köksoy. “A Fuzzy Modelling Approach to Robust Design via Loss Functions”. Turkish Journal of Forecasting 01, no. 2 (December 2017): 40-45.
EndNote Zeybek M, Köksoy O (December 1, 2017) A Fuzzy Modelling Approach to Robust Design via Loss Functions. Turkish Journal of Forecasting 01 2 40–45.
IEEE M. Zeybek and O. Köksoy, “A Fuzzy Modelling Approach to Robust Design via Loss Functions”, TJF, vol. 01, no. 2, pp. 40–45, 2017.
ISNAD Zeybek, Melis - Köksoy, Onur. “A Fuzzy Modelling Approach to Robust Design via Loss Functions”. Turkish Journal of Forecasting 01/2 (December 2017), 40-45.
JAMA Zeybek M, Köksoy O. A Fuzzy Modelling Approach to Robust Design via Loss Functions. TJF. 2017;01:40–45.
MLA Zeybek, Melis and Onur Köksoy. “A Fuzzy Modelling Approach to Robust Design via Loss Functions”. Turkish Journal of Forecasting, vol. 01, no. 2, 2017, pp. 40-45.
Vancouver Zeybek M, Köksoy O. A Fuzzy Modelling Approach to Robust Design via Loss Functions. TJF. 2017;01(2):40-5.

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