Fuzzy Development of Multiple Response Optimization
- 188 Downloads
This paper proposes a developed approach to Multiple Response Optimization (MRO) in two categories; responses without replicates and with some replicates based on fuzzy concepts. At first, the problem without any replicate in responses is investigated, and a fuzzy Decision Support System (DSS) is proposed based on Fuzzy Inference System (FIS) for MRO. The proposed methodology provides a fuzzy approach considering uncertainty in decision making environment. After calculating desirability of each response, total desirability of each experiment is measured by using values of each response desirability, applying membership function and fuzzy rules expressed by experts. Then Response Surface Methodology (RSM) is applied to fit a regression model between total desirability and controllable factors and optimize them. Next, a methodology is proposed for MRO with some replicates in responses which optimizes mean and variance simultaneously by applying fuzzy concepts. After introducing Deviation function based on robustness concept and using desirability function, a two objective problem is constituted. At last, a fuzzy programming is expressed to solve the problem applying degree of satisfaction from each objective. Then the problem is converted to a single objective model with the goals of increasing desirability and robustness simultaneously. The obtained optimum factor levels are fuzzy numbers so that a bigger satisfactory region could be provided. Finally, two numerical examples are expressed to illustrate the proposed methodologies for multiple responses without replicates and with some replicates.
KeywordsDesign of Experiments (DOE) Response Surface Methodology (RSM) Multiple Response Optimization (MRO) Fuzzy regression model Fuzzy Inference System (FIS)
Unable to display preview. Download preview PDF.
- Ames A, Mattucci N, McDonald S, Szonyi G, Hawkins D (1997) Quality loss function for optimization across multiple response surfaces. J Qual Technol 29: 339–346Google Scholar
- Chang HH (2008) A data mining approach to dynamic multiple responses in Taguchi experimental design. Expert Syst Appl (in press)Google Scholar
- Chiao C, Hamada M (2001) Analyzing experiments with correlated multiple responses. J Qual Technol 33: 451–465Google Scholar
- De Munck M, Moenens D, Desmet W, Vandepitte D (2008) A response surface based optimization algorithm for the calculation of fuzzy envelope FRFs of models with uncertain properties. Comput Struct (in press)Google Scholar
- Derringer G, Suich R (1980) Simultaneous optimization of several response variables. J Qual Technol 12: 214–219Google Scholar
- Kim K-J, Lin DKJ (1998) Dual response surface optimization: a fuzzy modeling approach. J Qual Technol 30: 1–10Google Scholar
- Ko YH, Kim KJ, Jun CH (2005) A new loss function-based method for multiresponse optimization. J Qual Technol 37: 50–59Google Scholar
- Lai YJ, Hwang CL (1992) Fuzzy multiple objective decision making. Springer, BerlinGoogle Scholar
- Luenberger DG (1989) Linear and nonlinear programming, 2nd edn. Addison-Wesley, ReadingGoogle Scholar
- Montgomery DC (2005) Design and analysis of experiments, 6th edn. Wiley, New YorkGoogle Scholar
- Vining G (1998) A compromise approach to multi response optimization. J Qual Technol 30: 309–313Google Scholar