A novel approach for non-normal multi-response optimisation problems

Abstract

Various creative multi-response optimisation approaches have been developed in the literature. Most of these researches are based on the normality assumption of the response distribution. However, this assumption does not necessarily hold in some real cases, such as non-normal multiple responses. Also, the reproducibility of optimisation results does not hold in some practical applications due to the variability of predicted responses associated with model uncertainty. In this paper, a novel approach is proposed to address the issues for non-normal multi-response optimisation. The proposed method not only identifies significant effects for each response by incorporating factorial effect principles into the framework of the Bayesian generalised linear models (GLMs) but also takes into account the model uncertainty and the variability of predicted responses by using the Bayesian sampling technique and Pareto optimal strategy. Furthermore, the optimal parameter settings are found by using grey incidence analysis (GIA). Besides, two examples are used to illustrate the effectiveness of the proposed method. The results show that the proposed method not only effectively identify significant factors but also find more satisfactory parameter settings when the reliability and reproducibility of optimisation results are considered simultaneously.

KEYWORDS:

• Quality management
• non-normal multi-response
• generalized linear models
• Bayesian analysis
• factorial effect principle

Disclosure statement

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

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (NSFC) [grant numbers: 71771121, 71931006, 72072089], and Natural Sciences and Engineering Research Council of Canada (NSERC) [grant number: RGPIN-2018-03862].

Notes on contributors

Jianjun Wang

Jianjun Wang is an Associate Professor of the Department of Mangement Science and Engineering at Nanjing University of Science and Technology. He received his BSc in Applied Mathematics from Jishou University, China, and his MSc in Applied Statistics from Hunan University. He earned his Ph.D. in Quality Engineering from Nanjing University of Science and Technology, China. He is a member of QSR and INFORMS, and a senior member of Chinese Society of Optimization, Overall Planning and Economical Mathemics. He is a reviewer of some famous international journals such as JQT, EJOR, IJPR, CAIE and QTQM. His research interests include parameter design and optimisation, Bayesian statistics and modelling, industrial statistical and data analysis.

Yanan Tu

Yanan Tu earned her master's degree in Quality Engineering from Nanjing University of Science and Technology, China. Her research interests include the design of the experiment and data analysis.

Yan Ma

Ya Ma is a Ph.D. candidate in Quality Engineering from Nanjing University of Science and Technology, China. Her research interests include quality engineering and quality management.

Linhan Ouyang

Linhan Ouyang is an Associate professor in the Department of Management Science and Engineering, Nanjing University of Aeronautics and Astronautics, China. He earned his Ph.D. in Quality Engineering from Nanjing University of Science and Technology, China. His research interests include process modelling and design of experiments.

Yiliu Tu

Yiliu Tu is a professor at the Department of Mechanical and Manufacturing Engineering, University of Calgary, Canada, and Zi Jin Scholar Chair Professor at the School of Economics and Management, Nanjing University of Science and Technology, China. He received his BSc in electronic engineering and MSc in mechanical engineering, both from Huazhong University of Science and Technology (HUST), China; Ph.D. in production engineering from Aalborg University (AU), Denmark. His current research interests are OKP (One-of-a-Kind Production) product design and manufacture, ultra-fast laser micro-machining technology, project management, supply chain integration, and complex product life cycle quality assurance and control. He is a senior member of SME (Society of Manufacture Engineers) and a professional engineer of APEGA (The Association of Professional Engineers, Geologists, and Geophysicists of Alberta).