Monotonicity Analysis of Taguchi’s Robust Circuit Design Problem

Abstract

Taguchi’s robust circuit design problem can be formulated rigorously as an optimization problem. A necessary condition for optimality is that the control range be centered about the target value. This generates a constraint on the two design variables which cannot be solved for either variable. The present article shows that by approximating this unsolvable constraint with a simpler constraint that is solvable, one variable can be eliminated and the problem reduced to an unconstrained one in a single variable. Since this reduced objective turns out to be monotonic in the remaining design variable, its optimum value must be at the limit of its range. The corresponding optimum value of the other variable is then determined exactly from the true, not approximate, constraint. Since no model construction, experimentation, statistical analysis, or numerical iteration is needed, this procedure is recommended whenever the input-output relation is known to be a monotonic algebraic function.