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Abstract
Key Performance Indicators (KPIs) play an important role in comprehending and improving a manufacturing system. This article proposes a novel method using Ordered Block Model and Pair-Copula Construction (OBM-PCC) to approximate the multivariate distribution of KPIs. The KPIs are treated as random variables in the OBM and studied under the stochastic queuing framework. The dependence structure of the OBM represents the influence flow from system input parameters to KPIs. Based on the OBM structure, the PCC is employed to simultaneously approximate the joint probability density function represented by KPIs and quantify the KPI values. The OBM-PCC model removes the redundant pair-copulas in traditional modeling, at the same time enjoying the flexibility and desirable analytical properties in KPI modeling, thus efficiently providing the accurate approximation. Extensive numerical studies are presented to demonstrate the effectiveness of the OBM-PCC model.
Acknowledgements
We thank Shaw C. Feng from the Engineering Laboratory in National Institute of Standards and Technology for discussions and comments that greatly improved the manuscript.
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Notes on contributors
Chao Wang
Chao Wang is currently a Ph.D. student at the Department of Industrial and Systems Engineering, University of Wisconsin, Madison. He received his B.S. degree in measuring testing technologies and instruments from the Hefei University of Technology, Hefei, China, in 2012, and M.S. degree in test measurement technology and instrument from the University of Science and Technology of China, Hefei, China, in 2015. His research interests include statistical modeling, analysis and control for complex systems.
Shiyu Zhou
Shiyu Zhou is a professor in the Department of Industrial and Systems Engineering at the University of Wisconsin-Madison. He received his B.S. and M.S. in mechanical engineering from the University of Science and Technology of China in 1993 and 1996, respectively, and his master’s in industrial engineering and Ph.D. in mechanical engineering from the University of Michigan in 2000. His research interests include industrial analytics and system informatics by integrating statistics, system and control theory, and engineering knowledge for quality and productivity improvement. He has received numerous research grants from various federal agencies and industry companies. He is a recipient of a CAREER Award from the National Science Foundation and the Best Application Paper Award from IISE Transactions. He is a fellow of IISE, ASME, and SME.