Statistical Inference on Desirability Function Optimal Points to Evaluate Multi-Objective Response Surfaces
Abstract
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 2022
- Accession Number
- AD1181175
Entities
People
- Peter A. Calhoun
Organizations
- Air Force Institute of Technology