Multiple-target robust design with multiple functional outputs

Robust Parameter Design (RPD) is a quality improvement method to mitigate the effect of input noise on system output quality via adjustment of control and signal factors. This article considers RPD with multiple functional outputs and multiple target functions based on a time-consuming nonlinear simulator, which is a challenging problem rarely studied in the literature. The Joseph–Wu formulation of multi-target RPD as an optimization problem is extended to accommodate multiple functional outputs and use of a Gaussian Process (GP) emulator for the outputs. Due to computational demands in emulator fitting and expected loss function estimation posed by this big-data problem, a separable GP model is used. The separable regression and prior covariance functions, and the Cartesian product structure of the data are exploited to derive computationally efficient formulas for the posterior means of expected loss criteria for optimizing signal and control factors, and to develop a fast Monte Carlo procedure for building credible intervals for the criteria. Our approach is applied to an example on RPD of a coronary stent for treating narrowed arteries, which allows the optimal signal and control factor settings to be estimated efficiently. Supplementary materials are available for this article. Go to the publisher’s online edition of IISE Transactions, datasets, additional tables, detailed proofs, etc.