Cost-Driven Parameter Design

Parameter design methodology has focused primarily on the quadratic loss function, which can often be solved by using a two-step procedure involving the minimization of a dispersion measure and then adjusting the mean to target. In some practical situations, however, the loss can be nonquadratic or highly skewed. By building on a theory of León and Wu, we develop a modeling and data-analysis strategy for a general loss function, in which the quality characteristic follows a location-scale model. The only difference from the two-step procedure just mentioned is the adjustment step, in which the mean is moved to that side of the target with lower cost. The technique is illustrated on an experiment involving epitaxial-layer growth in integrated-circuit fabrication.