A Fuzzy Modelling Approach to Robust Design via Loss Functions

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

Melis Zeybek , Onur Köksoy

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.

Keywords

fuzzy modeling, response surface methodology, robust parameter design, upside-down normal loss function

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).