Product and process yield estimation with Gaussian quadrature (GQ) reduction: Improvements over the GQ full factorial approach

Manufacturing or multivariate yield, the fraction of unscreened products which conforms to all product specification limits, is an important and commonly used metric for assessing and improving the quality of a production process. Current procedures for multivariate yield evaluation, such as Monte Carlo simulation, require substantial computing effort, making the iterative adjustment of design parameters often impractical. This paper introduces a new approach to multivariate yield evaluation based on a numerical integration procedure called Gaussian quadrature reduction. The advantage of this approach is a large reduction in the computational burden associated with multivariate yield evaluation with virtually no loss in accuracy of the estimates. The proposed procedure can be generalized to evaluate many other multivariate criteria such as expected costs and the desirability index. The method is demonstrated for three yield evaluation test problems, and comparisons to Monte Carlo-based evaluations are presented.