Design for nonsymmetrical statistical distributions

This paper presents a method for approximation of the constraint region and design centering for statistically distributed design parameters. Arbitrary uncorrelated probability density functions (p.d.f.'s) are considered, including truncated ones. The approximation problem is formulated deterministically and solved by optimization. The constraint region is approximated by a family of second-order ellipsoidal type functions. Formulation of the approximation problem takes into account statistical distributions of parameters, to be used in subsequent design centering. A special metric replaces evaluation of a multidimensional (yield) integral over the constraint region by simple integrals over fixed intervals. An additional outcome of the approximation process is location of a nominal design that increases yield.