Preferred Robust Response Surface Design with Missing Observations Based on Integrated TOPSIS-AHP Method

Missing observations occur in experimental designs as a result of insufficient sampling, machine breakdown, high cost, and errors in the measurements. In nanomanufacturing, missing observations often appear in designs because the combination of factors or molecular structures selected by a designer cannot be experimented successfully. In the current paper, Box-Behnken and face-centered composite designs were studied and eight robustness criteria including D-efficiency, tmax, tmax (1-α ), and their related sub-criteria were considered to evaluate the robustness of the aforementioned designs. Finally, the integrated TOPSIS-AHP methodology was employed to select the most suitable robust design, and a numerical example was also presented to assess the applicability of the proposed approach.