A coupled robust design using game theory

Robust design is a proven process to achieve insensitivity. From the view point of numerical optimization, the robustness of the objective function makes the system performance insensitive to uncertainties. To better manage the uncertainties, the Taguchi method, reliability-based optimization and robust optimization can be used. This study suggests how to analyze a robust design problem using axiomatic design concept. The design axioms provide a general framework for design methodologies. Two axioms are (1) Independence Axiom and (2) Information Axiom. These axioms can be applied to all design processes in a general way. The first axiom illustrates the relationship between functional requirements (FRs) and design parameters (DPs). Then, the designs of products can be classified into three types: uncoupled, decoupled and coupled. Two goals of robust design can be defined as two functional requirements. One is to reduce the distribution of a response. The other is to set the mean of a response to its target. In general, it is easy to determine the robust solution for a uncoupled or decoupled design. However, the coupled design cannot currently give true robustness, leading to a trade-off between performance and robustness. In this paper, game theory is applied to optimize the trade-off between two functional requirements.