An interval approach to robust design with parameter uncertainty

Abstract

In robust design, it is common to estimate empirical models that relate an output response variable to controllable input variables and uncontrollable noise variables from experimental data. However, when determining the optimal input settings that minimise output variability, parameter uncertainties in noise factors and response models are typically neglected. This article presents an interval robust design approach that takes parameter uncertainties into account through the confidence regions for these unknown parameters. To avoid obtaining an overly conservative design, the worst and best cases of mean squared error are both adopted to build an optimisation approach. The midpoint and radius of the interval are used to measure the location and dispersion performances, respectively. Meanwhile, a data-driven method is applied to obtain the relative weights of the location and dispersion performances in the optimisation approach. A simulation example and a case study using automobile manufacturing data from the dimensional tolerance design process are used to demonstrate the effectiveness of the proposed approach. The proposed approach of considering both uncertainties is shown to perform better than other approaches.

Keywords:

• robust parameter design
• confidence region
• interval analysis
• parameter uncertainty
• location and dispersion performances

Acknowledgements

We would like to thank the Associate Editor and two anonymous referees for their many valuable comments, which led to significant improvements in the article. We also acknowledge Hui Zeng for encouragement and fruitful discussions, who is a senior dimensional engineer of Ford Motor Research & Engineering (Nanjing) Co., Ltd.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China under grants NSFC [grant number 71471088], [grant number 71371099], [grant number 71211140350]; the National Research Foundation of Korea under grant NRF [grant number 2012K1A2B1A03000793]; the Basic Science Research Programme through NRF, funded by the Ministry of Science, ICT & Future Planning of Korea [grant number 2013062959], which are gratefully acknowledged.