Abstract

Computer experiments using deterministic simulators are often used to supplement physical system experiments. A common problem is that a computer simulator may provide biased output for the physical process due to the simplified physics or biology used in the mathematical model. However, when physical observations are available, it may be possible to use these data to align the simulator output to be close to the true mean response by constructing a bias-corrected predictor (a process called calibration). This talk looks at two aspects of experimental design for prediction of physical system means using a Bayesian calibrated predictor. First, the empirical prediction accuracy over the output space of several different types of combined physical and simulator designs is discussed. In particular, designs constructed using the integrated mean squared prediction error seem to perform well. Secondly, a sequential design methodology for optimizing a physical manufacturing process when there are multiple, competing product objectives is described. The goal is to identify a set of manufacturing conditions each of which leads to outputs on the Pareto Front of the product objectives, i.e. identify manufacturing conditions which cannot be modified to improve all the product objectives simultaneously. A sequential design methodology which maximizes the posterior expected minimax fitness function is used to add data from either the simulator or the manufacturing process. The method is illustrated with an example from an injection molding study. The presentation is based on joint work with Thomas Santner, Erin Leatherman, and Po-Hsu Allen Chen.