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

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.

KEYWORDS:

• Robust design
• loss function
• noise factors
• computer experiments
• shifted log transform

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Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Research Grants Council of Hong Kong, China [General Research Fund Project Nos.: CityU 11226716; CityU 11201117; CityU 11205118; CityU 11201519].

Notes on contributors

Fan Jiang

Fan Jiang is a PhD student in the School of Data Science at City University of Hong Kong. She received her B.S. degree from the Department of Automation, Huazhong University of Science and Technology, Wuhan, China. Her research interest is design and analysis of computer experiments.

Matthias Hwai-Yong Tan

Matthias Hwai-Yong Tan is an associate professor in the School of Data Science at City University of Hong Kong. He received a BEng in mechanical-industrial engineering from the Universiti Teknologi Malaysia, an MEng in industrial and systems engineering from the National University of Singapore and a PhD in industrial and systems engineering from Georgia Institute of Technology. His research interests include uncertainty quantification and applied statistics.