A Bayesian Approach for Multiple Response Surface Optimization in the Presence of Noise Variables

Area of Science:

• Engineering
• Statistics
• Operations Research

Background:

• Traditional parameter design struggles with multiple response constraints and noise variability.
• Existing methodologies may not adequately address robustness in complex systems.
• Peterson's (2000) methodology provides a foundation for robust design.

Purpose of the Study:

• To present a Bayesian approach for the multiple response robust parameter design problem.
• To develop a method that maximizes the posterior predictive probability of satisfying response constraints.
• To ensure solutions are robust to variations in noise variables.

Main Methods:

• Bayesian framework maximizing posterior predictive probability of constraint satisfaction.
• Integration of predictive density over response and noise variables for robustness.
• Evaluation of two methods for solving the maximization problem involving Monte Carlo integrations.

Main Results:

• A novel approach for robust parameter design is successfully developed.
• Matlab code enables rapid identification of optimal, robust solutions.
• The method is validated using two illustrative examples from existing literature.

Conclusions:

• The proposed Bayesian method effectively addresses multiple response robust parameter design.
• The integration over noise variables enhances solution robustness.
• The developed computational tool facilitates practical application of the robust design methodology.