Performance Distribution Analysis and Robust Design

Abstract

The paper presents the theory of performance sensitivity distribution and a novel robust parameter design technique. In the theory, a Jacobian matrix describes the effect of the component tolerance to the system performance, and the performance distribution is characterized in the variation space by a set of eigenvalues and eigenvectors. Thus, the feasible performance space is depicted as an ellipsoid. The size, shape, and orientation of the ellipsoid describe the quantity as well as quality of the feasible space and, therefore, the performance sensitivity distribution against the tolerance variation. The robustness of a design is evaluated by comparing the fitness between the ellipsoid feasible space and the tolerance space, which is a block, through a set of quantitative and qualitative indexes. The robust design can then be determined. The design approach is demonstrated in a mechanism design problem. Because of the generality of the analysis theory, the method can be used in any design situation as long as the relationship between the performance and design variables can be expressed analytically.