Integration of game theory and response surface method for robust parameter design

Robust parameter design (RPD) is to determine the optimal controllable factors that minimize the variation of quality performance caused by noise factors. The dual response surface approach is one of the most commonly applied approaches in RPD that attempts to simultaneously minimize the process bias (i.e., the deviation of the process mean from the target) as well as process variability (i.e., variance or standard deviation). In order to address this tradeoff issue between the process bias and variability, a number of RPD methods are reported in literature by assigning relative weights or priorities to both the process bias and variability. However, the relative weights or priorities assigned are often subjectively determined by a decision maker (DM) who in some situations may not have enough prior knowledge to determine the relative importance of both the process bias and variability. In order to address this problem, this paper proposes an alternative approach by integrating the bargaining game theory into an RPD model to determine the optimal factor settings. Both the process bias and variability are considered as two rational players that negotiate how the input variable values should be assigned. Then Nash bargaining game solution technique is applied to determine the optimal, fair, and unique solutions (i.e., a balanced agreement point) for this game. This technique may provide a valuable recommendation for the DM to consider before making the final decision. This proposed method may not require any preference information from the DM by considering the interaction between the process bias and variability. To verify the efficiency of the obtained solutions, a lexicographic weighted Tchebycheff method which is often used in bi-objective optimization problems is utilized. Finally, in two numerical examples, the proposed method provides non-dominated tradeoff solutions for particular convex Pareto frontier cases. Furthermore, sensitivity analyses are also conducted for verification purposes associated with the disagreement and agreement points.