Quality design based on kernel trick and Bayesian semiparametric model for multi-response processes with complex correlations

ABSTRACTProcesses or products are typically complex systems with numerous interrelated procedures and interdependent components. This results in complex relationships between responses and input factors, as well as complex nonlinear correlations among multiple responses. If the two types of complex correlations in the quality design cannot be properly dealt with, it will affect the prediction accuracy of the response surface model, as well as the accuracy and reliability of the recommended optimal solutions. In this paper, we combine kernel trick-based kernel principal component analysis, spline-based Bayesian semiparametric additive model, and normal boundary intersection-based evolutionary algorithm to address these two types of complex correlations. The effectiveness of the proposed method in modeling and optimisation is validated through a simulation study and a case study. The results show that the proposed Bayesian semiparametric additive model can better describe the process relationships compared to least squares regression, random forest regression, and support vector basis regression, and the proposed multi-objective optimisation method performs well on several indicators mentioned in the paper.KEYWORDS: Quality designBayesian inferencerandom walk priortensor B splinesemiparametric additive model Disclosure statementNo potential conflict of interest was reported by the author(s).Data availability statementThe data used to support the findings of the case study can be downloaded from the website https://figshare.com/articles/dataset/DATA_xlsx/22567336.Additional informationFundingThis work is supported by National Natural Science Foundation of China [grant numbers: 72301002, 72071001, 72171118]; Humanities and Social Sciences Planning Project of the Ministry of Education [grant numbers: 20YJAZH066, 21YJCZH148]; Excellent Young Talent Project of in Colleges and Universities of Anhui Province [grant number: gxyqZD2022001]; Science and Technology Project of Jiangxi Provincial Education Department [grant number: GJJ210528].Notes on contributorsShijuan YangShijuan Yang is a lecturer of School of Business at Anhui University, Hefei, China. She earned her Ph.D in Quality Management and Quality Engineering from Nanjing University of Science and Technology, China. Her research interests include applied statistics and quality management.Jianjun WangJianjun Wang is a Professor at the Department of Management Science and Engineering, Nanjing University of Science and Technology, China. He is a senior member of the Chinese Society of Optimization, Overall Planning, and Economical Mathematics. He is a reviewer of several international journals such as JQT, EJOR, IJPR, CAIE, and QTQM. His current research interests include quality engineering and quality management, robust parameter design, Bayesian modeling and optimisation, and industrial statistics.Xiaoying ChengXiaoying Chen is a Ph.D. candidate in Quality Management and Quality Engineering from Nanjing University of Science and Technology, China. Her research interests include Bayesian statistics and quality management and quality engineering.Jiawei WuJiawei Wu is a full lecturer at the School of Information Management, Jiangxi University of Finance and Economics, Nanchang, China. He has held visiting appointments at the University of Toronto in Canada. He has authored or coauthored more than 15 journal papers in the fields of quality and reliability engineering, optimisation design, and product development.Jinpei LiuJinpei Liu is a professor of School of Business at Anhui University, China. He received his Ph.D. in management science and engineering from Tianjin University in 2012, an MSc in probability and operations research from Anhui University in 2008 and a BSc in Statistics from Anhui University in 2005. His current research interests include forecasting, applied statistics and big data analysis. He is a reviewer of some famous international journals such as EJOR, CAIE, IEEE TEM and IEEE TFS.