Date of Award
Doctor of Philosophy (PhD)
Department of Mathematics and Statistics
Beau A. Nunnally, PhD
A shortfall of the Derringer and Suich (1980) desirability function is lack of inferential methods to quantify uncertainty. Most articles for addressing uncertainty usually involve robust methods, providing a point estimate that is less affected by variation. Few articles address confidence intervals or bands but not specifically for the Derringer and Suich method. This research provides two valuable contributions to the field of response surface methodology. The first contribution is evaluating the effect of correlation and plane angles on Derringer and Suich optimal solutions. The second contribution proposes and compares 8 inferential methods--both univariate and multivariate--for creating confidence intervals on each desirability function solution for first order and second order models. The effect of the Derringer and Suich method parameters, objective plane angles, and differing correlation between response surfaces are examined through simulation. The 8 proposed methods include a simple best/worst case method, 2 generalized methods, 4 simulated surface methods, and a nonparametric bootstrap method. One of the generalized methods, 2 of the simulated surface methods, and the nonparametric method account for covariance between the response surfaces. Bivariate examples showcase these methods in the first order and second order models. A multivariate real-world case with 3 objectives is also examined. While all 7 novel methods and the best/worst method seem to perform decently on the second order models. The methods which utilize an underlying multivariate-t distribution, Multivariate Generalized (MG) and Multivariate t Simulated Surface (MVtSSig), are recommended methods from this research as they perform well with small samples for both first order and second order models with coverage only becoming unreliable at non-optimal solutions. MG and MVtSSig inference should be used in conjunction with robust methods such as Pareto Front Optimization to help ascertain which solutions are more likely to be optimal before constructing confidence interval.
DTIC Accession Number
Calhoun, Peter A., "Statistical Inference on Desirability Function Optimal Points to Evaluate Multi-Objective Response Surfaces" (2022). Theses and Dissertations. 5545.