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

#### Akın Özdemir [1]

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.

Quality by design, computer-aided design, optimum operating condition, mixed integer linear programming, optimization
• 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.
Birincil Dil en Mühendislik, Ortak Disiplinler Makaleler Yazar: Akın Özdemir (Sorumlu Yazar)Kurum: BAYBURT UNIVERSITYÜlke: Turkey Yayımlanma Tarihi : 30 Haziran 2019
 Bibtex @araştırma makalesi { umagd497045, journal = {International Journal of Engineering Research and Development}, issn = {}, eissn = {1308-5514}, address = {Kırıkkale Üniversitesi Mühendislik Fakültesi Dekanlığı Kampüs 71450 Yahşihan/KIRIKKALE}, publisher = {Kırıkkale Üniversitesi}, year = {2019}, volume = {11}, pages = {551 - 559}, doi = {10.29137/umagd.497045}, title = {A Mixed Integer Linear Programming Model for Finding Optimum Operating Conditions of Experimental Design Variables Using Computer-Aided Optimal Experimental Designs}, key = {cite}, author = {Özdemir, Akın} } APA Özdemir, A . (2019). A Mixed Integer Linear Programming Model for Finding Optimum Operating Conditions of Experimental Design Variables Using Computer-Aided Optimal Experimental Designs. International Journal of Engineering Research and Development , 11 (2) , 551-559 . DOI: 10.29137/umagd.497045 MLA Özdemir, A . "A Mixed Integer Linear Programming Model for Finding Optimum Operating Conditions of Experimental Design Variables Using Computer-Aided Optimal Experimental Designs". International Journal of Engineering Research and Development 11 (2019 ): 551-559 Chicago Özdemir, A . "A Mixed Integer Linear Programming Model for Finding Optimum Operating Conditions of Experimental Design Variables Using Computer-Aided Optimal Experimental Designs". International Journal of Engineering Research and Development 11 (2019 ): 551-559 RIS TY - JOUR T1 - A Mixed Integer Linear Programming Model for Finding Optimum Operating Conditions of Experimental Design Variables Using Computer-Aided Optimal Experimental Designs AU - Akın Özdemir Y1 - 2019 PY - 2019 N1 - doi: 10.29137/umagd.497045 DO - 10.29137/umagd.497045 T2 - International Journal of Engineering Research and Development JF - Journal JO - JOR SP - 551 EP - 559 VL - 11 IS - 2 SN - -1308-5514 M3 - doi: 10.29137/umagd.497045 UR - https://doi.org/10.29137/umagd.497045 Y2 - 2019 ER - EndNote %0 Uluslararası Mühendislik Araştırma ve Geliştirme Dergisi A Mixed Integer Linear Programming Model for Finding Optimum Operating Conditions of Experimental Design Variables Using Computer-Aided Optimal Experimental Designs %A Akın Özdemir %T A Mixed Integer Linear Programming Model for Finding Optimum Operating Conditions of Experimental Design Variables Using Computer-Aided Optimal Experimental Designs %D 2019 %J International Journal of Engineering Research and Development %P -1308-5514 %V 11 %N 2 %R doi: 10.29137/umagd.497045 %U 10.29137/umagd.497045 ISNAD Özdemir, Akın . "A Mixed Integer Linear Programming Model for Finding Optimum Operating Conditions of Experimental Design Variables Using Computer-Aided Optimal Experimental Designs". International Journal of Engineering Research and Development 11 / 2 (Haziran 2019): 551-559 . https://doi.org/10.29137/umagd.497045 AMA Özdemir A . A Mixed Integer Linear Programming Model for Finding Optimum Operating Conditions of Experimental Design Variables Using Computer-Aided Optimal Experimental Designs. IJERAD. 2019; 11(2): 551-559. Vancouver Özdemir A . A Mixed Integer Linear Programming Model for Finding Optimum Operating Conditions of Experimental Design Variables Using Computer-Aided Optimal Experimental Designs. International Journal of Engineering Research and Development. 2019; 11(2): 559-551.