The basic principle of robust parameter design (RPD) is to determine the optimal values of a set of controllable parameters that minimize the quality performance fluctuations caused by noise factors. The dual response surface method is one of the most widely applied approaches in RPD that tries to simultaneously minimize the deviation of the process mean from target and the process variance. However, there are situations when a compromise between the process mean and process variance is necessary, then the trade-off between them becomes an intractable problem. In order to solve the problem, we introduce a method that attempts to integrate the bargaining game theory concept into RPD to determine the optimal solutions. To verify the efficiency of our proposed method, the lexicographic weighted Tchebycheff method is applied to identify if the calculated solution is on the associated Pareto frontier. Two numerical examples show that our model works well in convex frontier cases. Lastly, several sensitivity analyses are conducted to examine the effect of the disagreement point value on the final solution.
Abstract The basic principle of robust parameter design (RPD) is to determine the optimal values of a set of controllable parameters that minimize the quality performance fluctuations [...]
Robust design has received a great deal of attention from quality researchers in recent years, and a number of optimization methodologies based on the dual response format have been proposed. The majority of existing bi-objective optimization models concentrate on the trade-offs between the process mean and variability functions without investigating the interactions between control factors and quality characteristics. The primary objective of this research is to integrate the Stackelberg leadership model into the robust design procedure and propose a Stackelberg game-based robust design (SGRD) method to determine appropriate control factor settings by minimizing the values of desired optimization targets based on an analysis of possible combinations of input and output quality parameters. Herein, first, a bi-objective robust design optimization problem is formulated as a dual response model using response surface methodology (RSM). Second, the proposed SGRD model is developed via decomposition into two leader-follower game models. Finally, the mean square error (MSE) criterion is applied to evaluate models, and select non-dominated solutions in various situations. Numerical examples are used to demonstrate that the proposed method provides significant solutions in cases containing unidentified priorities between the dual responses and undiscovered correlations among several inputs and outcomes. In addition, according to the case study analysis, the proposed method is more efficient than the conventional dual response approach when dealing with bi-objective robust design optimization problems.
Abstract Robust design has received a great deal of attention from quality researchers in recent years, and a number of optimization methodologies based on the dual response format [...]
Integration of game theory and response surface method for robust parameter design 
