Robust design optimization with bivariate quality characteristics

In robust design optimization, if Taguchi quality loss function is employed, its expectation is minimized. When multiple quality characteristics exist, their covariances appear in the expectation and usually require numerical integrations. In this work, we propose an analytical robust design approach without numerical integrations to problems with bivariate quality characteristics. The quality characteristics are assumed to be functions of independent normal random variables with small uncertainties. Because the uncertainties are small, the functions are linearized with good accuracy. Analytical equations are then derived for the expected quality loss. The approach is efficient because no numerical integrations are needed. It is applied to the robust synthesis of a four-bar linkage.