Robust design optimization for multiple characteristic problems

Robust design is an important method for improving product or manufacturing process design by making the output response insensitive (robust) to difficult-to control variations (noise). Most research in robust design has focused on problems with a single characteristic or response. This paper concerns the application of a robust design method to problems with multiple characteristics. We extend the multivariate loss considered by Pignatiello to include the smaller- and largerthe-better type characteristics. Under various assumptions, we develop appropriate two-step procedures that minimize the average multivariate loss. Similar to the advantages in the single characteristic problem, the proposed two-step procedures substantially reduce the dimension of the design optimization problem and allow for future changes of response target values without re-optimization. We illustrate the proposed procedures with a polysilicon deposition example.