A central composite design is a good choice for a spherical design region while providing high-quality predictions over the entire spherical design region. However, this design requires design variable settings outside the range of the design variables in the factorial part. On the other hand, a face-centered design provides high-quality prediction over the entire cuboidal design region and does not require using design points outside the factorial ranges. Therefore, a face-centered design is preferred over other designs. In the literature, controllable input variables have been addressed. However, both controllable and noise input variables have been paid little attention. The aim is to build regression models for both the process mean and variance. The next task is to obtain an optimal operating condition for both controllable and noise input variables. A weighted mean-squared error optimization model is proposed. Comparison studies are conducted while considering different weights for each component of the objective function. Finally, the proposed methodology is an effective technique to obtain optimal settings for a cuboidal design region.

Keywords - Quality Engineering, Weighted Mean-Squared Error Model, Controllable Input Variables, Noise Input Variables, Face-Centered Design, Optimization

[1] G. G. Vining and R. H. Myers, “Combining Taguchi and response surface philosophies: a dual response approach,” J. Qual. Technol., vol. 22(1), pp. 38-45, 1990.
[2] R. H. Myers and W. H. Carter, “Response surface techniques for dual response systems,” Technometrics, vol. 15(2), pp. 301-317, 1973.
[3] E. Del Castillo and D. C. Montgomery, “A nonlinear programming solution to the dual response problem,” J. Qual. Technol., vol. 25(3), pp. 199-204, 1993.
[4] D. K. Lin and W. Tu, “Dual response surface optimization,” J. Qual. Technol., vol. 27(1), pp. 34-39, 1995.
[5] K. A. Copeland and P. R. Nelson, “Dual response optimization via direct function minimization,” J. Qual. Technol., vol. 28(3), pp. 331-336, 1996.
[6] O. Köksoy and N. Doganaksoy, “Joint optimization of mean and standard deviation using response surface methods,” J. Qual. Technol., vol. 35(3), pp. 239-252, 2003.
[7] L. Ouyang, Y. Ma, J. H. Byun, J. Wang, and Y. Tu, “An interval approach to robust design with parameter uncertainty,” Int. J. Prod. Res., vol. 54(11), pp. 3201-3215, 2016.
[8] A. Ozdemir and B. R. Cho, “A Nonlinear integer programming approach to solving the robust parameter design optimization problem,” Qual. Reliab. Eng. Int., vol. 32(8), pp. 2859-2870, 2016.
[9] A. Ozdemir and B. R. Cho, “Response surface-based robust parameter design optimization with both qualitative and quantitative variables.” Eng. Optimiz., vol. 49(10), pp. 1796-1812, 2017.
[10] A. Ozdemir and B. R. Cho, “Response surface optimization for a nonlinearly constrained irregular experimental design space,” Eng. Optimiz., vol. 51(12), pp. 2030-2048, 2019.
[11] T. N. Tsai and M. Liukkonen, “Robust parameter design for the micro-BGA stencil printing process using a fuzzy logic-based Taguchi method,” Appl. Soft Comput., vol. 48, pp. 124-136, 2016.
[12] A. Hot, T. Weisser, and S. Cogan, “An info-gap application to robust design of a prestressed space structure under epistemic uncertainties,” Mech. Syst. Signal Pr., vol. 91, pp. 1-9, 2017.
[13] Y. Lu, S. Wang, C. Yan, and Z. Huang, “Robust optimal design of renewable energy system in nearly/net zero energy buildings under uncertainties,” Appl. Energ., vol. 187, pp. 62-71, 2017.
[14] K. Chatterjee, K. Drosou, S. D. Georgiou, and C. Koukouvinos, “Response modelling approach to robust parameter design methodology using supersaturated designs,” J. Qual. Technol., vol. 50(1), pp. 66-75, 2018.
[15] R. H. Myers, D. C. Montgomery, and C. M. Anderson-Cook, Response Surface Methodology: Process and Product Optimization Using Designed Experiments (Wiley Series in Probability and Statistics), Hoboken, NJ: Wiley, 2016.