Yield Maximization and Worst-Case Design with Arbitrary Statistical Distributions

We describe a method by which a variety of statistical design problems can be solved by a linear program. We describe three key aspects of this approach. 1) The correspondence between the level contours of a given probability density function and a particular norm, which we shall call a pdf-norm. 2) The expression of distance in this norm from a given set of hyperplanes in terms of the dual of the pdf-norm. 3) The use of a linear program to inscribe a maximal pdf-norm-body into a simplicial approximation to the feasible region of a given statistical design problem. This work thus extends the applicability of a previously published algorithm, to the case of arbitrary pdf-norms and consequently to a wide variety of statistical design problems including the common mixed worst-case-yield maximization problem. © 1980 IEEE