Necessary conditions for optimization of multiple response functions and a new multiple response surface methodology

The focus of this dissertation is the application of multiple response optimization (optimization of multiple quality characteristics). There are three key results: development of a structure for categorizing and evaluating multiple response surface methodologies (MRSM); development of the necessary conditions and assumptions for application of a combined MRSM; and the development of a new combined weighted multi-response optimization methodology. The basic framework for categorizing multiple response optimization methodologies includes the type of approach (combined and constrained), number and type of response variables (means and standard deviations), and the method of preference elicitation.; A major result is the identification of the assumptions and necessary conditions that are required for the application of combined methodologies. Although several authors have cited the requirement of statistical independence for application of their methodology, it is shown that correlation and statistical independence are arbitrary and not relevant conditions. Rather, other conditions, not identified in earlier research, are necessary for application of a combined methodology, including monotonicity of preference, mutual preferential independence, and use of appropriate value functions. Each of the available combined methodologies is analyzed, yielding the strengths and weaknesses of each methodology and the conditions that must be satisfied to apply the methodology. It is shown that several of the available combined methodologies generate dominated solutions. Most of the available methodologies are restricted to a limited number of types of problems that can be solved using the methodology.; A new, theoretically-based, combined methodology for optimizing multiple response functions, the weighted multi-response optimization (WMRO) methodology, is developed and presented. Conditions required for application of the WMRO methodology are developed and presented. The WMRO methodology uses decision-maker-specified preferences among the responses to generate weights, assuring the identification of the most preferred nondominated solution, when the response objectives are convex. Additionally, the WMRO methodology is a straightforward approach that can be implemented easily using an Excel spreadsheet with Solver. Several examples of the application of the WMRO methodology are provided and the results obtained using the WMRO methodology are compared with the results obtained using other appropriate combined methodologies available from the literature.