Robust monitoring of stochastic textured surfaces

Abstract

Stochastic textured surfaces (STSs) do not have well-defined features, and their quality characteristics are reflected through the stochastic nature of their surface textures. Monitoring general global changes in the stochastic nature of STSs is a relatively new, yet important problem. The limited literature for solving this problem has not considered the common situation in which the normal, in-control STS data are subject to structured surface-to-surface variation in their stochastic nature, due to the challenging nature of this problem. In this paper, we propose a dissimilarity-based multivariate control charting approach for monitoring general global changes in STSs in the presence of such structured in-control variation. Our approach is novel in that it quantifies the level of abnormality from multiple ‘spanning points’, instead of a single reference as in prior work. The spanning points are selected via dissimilarity-based manifold learning and space filling sampling methods. We test our approach with simulated and real textile examples and demonstrate its superior robustness to the structured in-control variation. Our approach has potential to provide a general control charting framework for any applications involving complex data structures other than STS data.

KEYWORDS:

• Dissimilarity
• outlier detection
• Phase I analysis
• statistical process control (SPC)
• variation

Disclosure statement

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

Notes

1 To simplify the discussion, we assume any variation in the retained set of N_train STS images is IC. In practice, it may be necessary to visualize the variation patterns as done in Bui and Apley (2019). This helps identify the root causes of the variation and address them until only IC variation is left. The Phase I stability analysis would be then reapplied to a new set of Phase I STS images acquired from the improved manufacturing process.

2 Note that OC behavior can occur in dimensions other than the IC variation dimension, and therefore the IC region of a control chart has an ellipsoidal shape.

Additional information

Funding

This work was supported in part by Air Force Office of Scientific Research Grant #313-0866-02//FA9550-18-1-0381, which the authors gratefully acknowledge.

Notes on contributors

Anh Tuan Bui

Anh Tuan Bui received the B.S. degree in electrical engineering from Hanoi University of Science and Technology, Hanoi, Vietnam, the M.S. degree in industrial and management engineering from Pohang University of Science and Technology, Pohang, South Korea, and the Ph.D. degree in industrial engineering & management sciences from Northwestern University, Evanston, IL. He is currently an Assistant Professor in the Department of Statistical Sciences & Operations Research at Virginia Commonwealth University, Richmond, VA. His research interests lie in statistical learning, industrial statistics, and data analytics for applications in manufacturing, materials, and enterprise engineering, using large and complex data structures. Dr Bui is a member of the Institute for Operations Research and the Management Sciences (INFORMS). He is a recipient of the Lloyd S. Nelson Award (American Society for Quality).

Daniel W. Apley

Daniel W. Apley is a Professor of Industrial Engineering and Management Sciences at Northwestern University, Evanston, IL. His research interests are at the interface of engineering modelling, statistical analysis, and machine learning, with particular emphasis on manufacturing and enterprise operations in which large amounts of data are available. He is a fellow of the American Statistical Association. He received the NSF CAREER award in 2001, the IIE Transactions Best Paper Award in 2003, the Wilcoxon Prize for best practical application paper appearing in Technometrics in 2008, and the Lloyd S. Nelson Award for the paper with the greatest immediate impact to practitioners appearing in the Journal of Quality Technology in 2018. He has served as Editor-in-Chief of Technometrics (2017–2020) and the Journal of Quality Technology (2009–2012), Chair of the Quality, Statistics & Reliability Section of INFORMS, and Director of the Manufacturing and Design Engineering Program at Northwestern.