Efficient Gradient-Based Optimization of Process Capability with Multiple, Potentially Nonnormal Outputs

Abstract

A process output has multiple performance measures (response variables) that are related to multiple input variables (both controllable and noise variables). The input variables are modeled as random variables and the relationships are modeled by transfer functions that may be known functional relationships or response surfaces that have been estimated from experimental data. The performance measures have specification limits. The goal is to select the target (or mean) values for the controllable input variables to minimize the weighted probabilities that the response variables will have values outside their specification limits without making distributional assumptions on the response variables. A single set of simulation replications is used to efficiently estimate derivatives of the weighted probability of defectives with respect to the parameters of the probability distributions of each input variable. These derivative estimates are used in a gradient-based optimization algorithm to select the mean values for the controllable input variables. The problem is motivated by and the algorithm is applied to the design and production of a resin to be used in the manufacture of an infant car seat.