Gaussian Processes with Input Location Error and Applications to the Composite Parts Assembly Process

This paper investigates Gaussian process modeling with input location error, where the inputs are corrupted by noise. Here, the best linear unbiased predictor for two cases is considered, according to whether there is noise at the target location or not. We show that the mean squared prediction error converges to a nonzero constant if there is noise at the target location, and we provide an upper bound of the mean squared prediction error if there is no noise at the target location. We investigate the use of stochastic Kriging in the prediction of Gaussian processes with input location error and show that stochastic Kriging is a good approximation when the sample size is large. Several numerical examples are given to illustrate the results, and a case study on the assembly of composite parts is presented. Technical proofs are provided in the appendices.