In robust design, associated with each quality characteristic,the design objective often involves multiple aspects such as"bringing the mean of performance on target"and "minimizingthe variations". Current ways of handling these multipleaspects using either the Taguchi's signal-to-noise ratio or theweighted-sum method are not adequate. In this paper, we solvebi-objective robust design problems from a utility perspectiveby following upon the recent developments on relating utilityfunction optimization to a Compromise Programming (CP)method. A robust design procedure is developed to allow adesigner express his/her preference structure of multiple aspectsof robust design. The CP approach, i.e., the Tchebycheffmethod, is then used to determine the robust design solutionwhich is guaranteed to belong to the set of efficient solutions(Pareto points). The quality utility at the candidate solution isrepresented by means of a quadratic function in a certain senseequivalent to the weighted Tchebycheff metric. The obtainedutility function can be used to explore the efficient solutions inthe neighborhood of the candidate solution. The iterative natureof our proposed procedure will assist decision making in qualityengineering and the applications of robust design.