Robust Parameter Designs in Computer Experiments Using Stochastic Approximation

Robust parameter designs are widely used to produce products/processes that perform consistently well across various conditions known as noise factors. Recently, the robust parameter design method is implemented in computer experiments. The structure of conventional product array design becomes unsuitable due to its extensive number of runs and the polynomial modeling. In this article, we propose a new framework robust parameter design via stochastic approximation (RPD-SA) to efficiently optimize the robust parameter design criteria. It can be applied to general robust parameter design problems, but is particularly powerful in the context of computer experiments. It has the following four advantages: (1) fast convergence to the optimal product setting with fewer number of function evaluations; (2) incorporation of high-order effects of both design and noise factors; (3) adaptation to constrained irregular region of operability; (4) no requirement of statistical analysis phase. In the numerical studies, we compare RPD-SA to the Monte Carlo sampling with Newton–Raphson-type optimization. An “Airfoil” example is used to compare the performance of RPD-SA, conventional product array designs, and space-filling designs with the Gaussian process. The studies show that RPD-SA has preferable performance in terms of effectiveness, efficiency and reliability.