A Quadrature-Based Sampling Technique for Robust Design With Computer Models

Several methods have been proposed for estimating transmitted variance to enable robust parameter design using computer models. This paper presents an alternative technique based on Gaussian quadrature which requires only 2n+1 or 4n+1 samples (depending on the accuracy desired) where n is the number of randomly varying inputs. The quadrature-based technique is assessed using a hierarchical probability model. The 4n+1 quadrature-based technique can estimate transmitted standard deviation within 5% in over 95% of systems which is much better than the accuracy of Hammersley Sequence Sampling, Latin Hypercube Sampling, and the Quadrature Factorial Method under similar resource constraints. If the most accurate existing method, Hammersley Sequence Sampling, is afforded ten times the number of samples, it provides approximately the same degree of accuracy as the quadrature-based method. Two case studies on robust design confirmed the main conclusions and also suggest the quadrature-based method becomes more accurate as robustness improvements are made.