Shifted log loss Gaussian process model for expected quality loss prediction in robust parameter design

Abstract

ABSTRACT Robust parameter design (RPD) aims at reducing the effect of noise variation on quality through achieving a small expected quality loss (EQL). In RPD with time-consuming computer simulations, Gaussian process (GP) models are used to predict the EQL. Three straightforward models for predicting the EQL include a GP model for the simulator output, a GP model for the quality loss, and a lognormal process model for the quality loss (the log quality loss is modeled as a GP). Each of these models has some drawbacks as discussed in this paper. We propose the shifted log loss GP model, which includes the lognormal process model for the quality loss and the GP model for the quality loss as special cases when the shift varies from zero to infinity. The proposed model overcomes some of the limitations of the three existing models. It has a simple and accurate approximation for the posterior EQL distribution, and it gives accurate and precise predictions of the EQL. We illustrate the superior performance of the proposed model over the three existing models with a toy example and an RPD problem involving a steel beam.