A review of robust design methods for multiple responses

Problems in engineering design often involve determining design variable settings to optimize individual product performance for multiple criteria, which are often in conflict. We review mathematically rigorous techniques from the statistical literature for finding a vector x of design variable settings, which produces an optimal compromise solution among a group of prioritized response variables. The best compromise solution is typically gained by optimizing an objective function, which incorporates the prioritized demands of multiple responses. Since most multi-response objective functions are constructed by combining the functions used to optimize univariate responses, a review of the prominent univariate approaches is presented first. A multivariate approach from the engineering literature called the compromise decision support problem (cDSP) is also reviewed. Finally, a table comparing the relative merits of the different multivariate approaches summarizes the article in a concise and user-friendly fashion.