A Mixed Integer Linear Programming Model for Finding Optimum Operating Conditions of Experimental Design Variables Using Computer-Aided Optimal Experimental Designs

Year 2019, Volume: 11 Issue: 2, 551 - 559, 30.06.2019

Akın Özdemir

https://doi.org/10.29137/umagd.497045

Cited By: 4

Abstract

Computer-aided
optimal experimental designs are an effective quality improvement tool that
provides insights of information under various quality engineering problems. In
the literature, considerable attention has been focused on maximizing the
determinant of the information matrix in order to generate optimal design
points. However, minimizing the average prediction based on the I-optimality criterion is more useful
than commonly used D-optimality
criterion for a number of situations. In this paper, special experimental
design situations are explored where both qualitative and quantitative input
variables are considered for an irregular design space with the pre-specified
number of design points and the first-order polynomial model. In addition, this
paper lays out the algorithmic foundations for the proposed D- and I-optimality criteria embedded mixed integer linear programming
models in order to obtain optimal operating conditions using the first-order
response functions. Comparative studies are also conducted. Finally, the
proposed models are superior to the traditional counterparts.

Keywords

Quality by design, computer-aided design, optimum operating condition, mixed integer linear programming, optimization

References

• Allen, T. T., & Tseng, S. H. (2011). Variance plus bias optimal response surface designs with qualitative factors applied to stem choice modeling. Quality and Reliability Engineering International, 27(8), 1199-1210.
• Arvidsson, M., & Gremyr, I. (2008). Principles of robust design methodology. Quality and Reliability Engineering International, 24(1), 23-35.
• Borkowski, J. J. (2003). A comparison of prediction variance criteria for response surface designs. Journal of Quality Technology, 35(1), 70-77.
• Box, G. E., & Draper, N. R. (1959). A basis for the selection of a response surface design. Journal of the American Statistical Association, 54(287), 622-654.
• Chatterjee, K., Drosou, K., Georgiou, S. D., & Koukouvinos, C. (2018). Response modelling approach to robust parameter design methodology using supersaturated designs. Journal of Quality Technology, 50(1), 66-75.
• Cook, R. D., & Nachtrheim, C. J. (1980). A comparison of algorithms for constructing exact D-optimal designs. Technometrics, 22(3), 315-324.
• Copeland, K. A., & Nelson, P. R. (1996). Dual response optimization via direct function minimization. Journal of Quality Technology, 28(3), 331-336.
• Del Castillo, E., & Montgomery, D. C. (1993). A nonlinear programming solution to the dual response problem. Journal of Quality Technology, 25(3), 199-204.
• Draper, N. R. (1982). Center points in second—order response surface designs. Technometrics, 24(2), 127-133.
• John, R. S., & Draper, N. R. (1975). D-optimality for regression designs: a review. Technometrics, 17(1), 15-23.
• Kiefer, J., & Wolfowitz, J. (1959). Optimum designs in regression problems. The Annals of Mathematical Statistics, 30(2), 271-294.
• Lin, D. K., & Tu, W. (1995). Dual response surface optimization. Journal of Quality Technology, 27(1), 34-39.
• Lu, Y., Wang, S., Yan, C., & Huang, Z. (2017). Robust optimal design of renewable energy system in nearly/net zero energy buildings under uncertainties. Applied Energy, 187, 62-71.
• Myers, R. H., Montgomery, D. C., & Anderson-Cook, C. M. (2016). Response Surface Methodology: Process and Product Optimization Using Designed Experiments (Wiley Series in Probability and Statistics).
• Ozdemir, A., & Cho, B. R. (2016). A nonlinear integer programming approach to solving the robust parameter design optimization problem. Quality and Reliability Engineering International, 32(8), 2859-2870.
• Ozdemir, A., & Cho, B. R. (2017). Response surface-based robust parameter design optimization with both qualitative and quantitative variables. Engineering Optimization, 49(10), 1796-1812.
• Park, G. J., Lee, T. H., Lee, K. H., & Hwang, K. H. (2006). Robust design: an overview. AIAA journal, 44(1), 181-191.
• Robinson, T. J., Borror, C. M., & Myers, R. H. (2004). Robust parameter design: a review. Quality and Reliability Engineering International, 20(1), 81-101.
• SAS Institute, 2013. Using JMP 11. SAS Institute. Cary, NC USA.
• Smith, K. (1918). On the standard deviations of adjusted and interpolated values of an observed polynomial function and its constants and the guidance they give towards a proper choice of the distribution of observations. Biometrika, 12(1/2), 1-85.
• Steinberg, D. M., & Bursztyn, D. (1998). Noise factors, dispersion effects, and robust design. Statistica Sinica, 8(1), 67-85.
• Toro Díaz, H. H., Chan, H. L., & Cho, B. R. (2012). Optimally designing experiments under non-standard experimental situations. International Journal of Experimental Design and Process Optimisation, 3(2), 133-158.
• Vining, G. G., & Myers, R. H. (1990). Combining Taguchi and response surface philosophies: a dual response approach. Journal of Quality Technology, 22(1), 38-45.
• Wald A. On the efficient design of statistical investigations. The Annals of Mathematical Statistics 1943; 14(2):134-140.