Bias-specified robust design optimization and its analytical solutions

Robust design has received consistent attention from researchers and practitioners for years, and a number of methodologies for robust design optimization have been reported in the research community. However, the majority of these existing methodologies ignore the case where the customer may tolerate and specify an upper bound on process bias. This paper proposes a bias-specified robust design method and formulates a nonlinear program that minimizes process variability subject to customer-specified constraints on the process bias using the ε-constrained method. This paper then derives the Karush–Khun–Tucker conditions and provides a solution procedure based on the Lagrangean method. A numerical example is provided for illustration.