Matching via majorization for consistency of product quality

Abstract

A new matching method is introduced in this paper to match attributes of parts in order to ensure consistent quality of products that are assembled from matched parts. The method yields invariant optimal matching that depends only on ranking of attributes of assembling parts, where the optimal matching criteria consist of a large class of metrics, including the Kantorovich cost function for matched pairs. Our method is non-parametric and based on the theory of majorization that reinforces a general rank-invariant matching strategy that ‘small matches with small and large matches with large’ for variance reduction. Using this majorization-based matching method, several specific multi-part matching problems are investigated in order to illustrate its wide applicability in quality assurance.

Keywords:

• Invariant optimal solutions
• matching pattern
• majorization
• Schur-convexity
• Kantorovich cost function

Acknowledgements

The authors would like to thank two anonymous referees and editor for their valuable suggestions on the improvements of the paper.

Notes

No potential conflict of interest was reported by the authors.

This work is in honor of Professor Alan G. Hawkes on his 75th birthday.

Additional information

Funding

This work was supported by the NSFC [grant number 71371031]; NSF [grant number DMS 1007556].