An online approach for robust parameter design with incremental Gaussian process

Abstract

Robust parameter design (RPD), an important method for quality improvement, can effectively mitigate the negative impact of fluctuations on product quality. Traditional RPD adopts offline design, that is, the optimal level of parameter combination is fixed by one-time modeling throughout the production process. This strategy is obviously unreasonable. Online RPD breaks through the limitation of traditional offline design, which can update the optimal setting by utilizing the new sample when the current optimal setting of controllable factors is not suitable. However, there are still some problems in the current version of online RPD, such as poor data fitting ability of response surface model and low efficiency of parameter design. In this paper, a new online RPD method based on Gaussian process (GP) is proposed. The GP model is used to construct the response surface, which has the capacity of dealing with high-dimensional nonlinear data. But traditional GP method adopts batch learning, it cannot update the model online with new samples. So this paper proposes an incremental Gaussian process model (IGP), which can update the response surface in real-time. In the proposed IGP based online robust parameter design method (IGP-RPD), an effective optimization strategy is used to find the optimal setting of controllable factors, and a reasonable selection criterion is used to determine the noise factor setting for the next stage. The optimal setting of the controllable factor in the previous stage and the currently observed noise factor are used as input, and the corresponding quality characteristic is taken as the output. The input and output form a new sample to update the response surface model. In this way, the RPD process can be redone continuously until the desirable optimal setting of the controllable factor is found. Three cases are used to verify the IGP-RPD method and compare it with the existing methods. The experiments manifest that the IGP-RPD method has better performance in both accuracy and efficiency.

Keywords:

• Gaussian process
• online strategy
• quality improvement
• response surface methodology
• robust parameter design

Data availability statement

The data that support the findings of this study are available in [EMULATION/PREDICTION] at [http://www.sfu.ca/∼ssurjano/index.html]. These data were derived from the following resources available in the public domain: [Cheng and Sandu (2010) Function, http://www.sfu.ca/∼ssurjano/chsan10.html; Dette and Pepelyshev (2010) 8-Dimensional Function, http://www.sfu.ca/∼ssurjano/detpep108d.html]. The authors confirm that the data supporting the findings of this study are available within the article [Montgomery, D. C. (2017). Design and analysis of experiments. John wiley & sons.].

Additional information

Funding

The funding provided for this study by the National Natural Science Foundation of China under Grant No.71872088, 71904078 and 71401080, the Social Science Foundation of Jiangsu under Grant No.17GLB016, the Postgraduate Research and Innovation Program of Jiangsu under Grant KYCX21_0837, the State Scholarship Fund of China under Grant NO.201508320059, “1311 Talent Fund” of NJUPT, the Science Foundation of Jiangsu under Grant No.BK20190793, the Project of Philosophy and Social Science Research in Colleges and Universities in Jiangsu Province under Grant No. 2018SJA0263 and Social Science Foundation of NJUPT under Grant No.NY218064 are gratefully acknowledged.

Notes on contributors

Xiaojian Zhou

Xiaojian Zhou is a professor and assistant dean in the Department of Management at the Nanjing University of Posts and Telecommunications. His research focuses on machine learning, statistics, quality management and computer experiment design.

Yunlong Gao

Yunlong Gao is a graduate student in the Department of Management at the Nanjing University of Posts and Telecommunications. His research interests involve machine learning, data analysis and robust parameter design theory.

Ting Jiang

Ting Jiang is an associate professor in the department of information engineering at the Nanjing University of Finance and Economics. Her research focuses on data mining, information retrieval, and recommendation systems of information systems.

Zebiao Feng

Zebiao Feng is an assistant professor in the Department of Management at the Nanjing University of Posts and Telecommunications. His research interests are quality management and quality engineering, applied statistics and computer experiment design.