Robust Design with Nonparametric Models: Prediction of Second-order Characteristics of Process Variability by Kriging

We use kriging to predict the mean and variance of a response y(x) when the input factors x are subject to random variability. Uncertainty on these predictions is obtained by considering fluctuations along one trajectory y of the process due to fluctuations of x, and then averaging over the possible trajectories, conditionally on input-output data. Possible applications include robust design engineering, where the data that are obtained from prototypes in laboratory experiments, or from simulation codes, are used to construct models for the responses of interest to the designer, but mass-production involves variability of input factors around the specifications the designer will indicate.