Nonparametric passenger flow monitoring using a minimum distance criterion

Abstract

Monitoring real-time passenger flow in urban rapid transit systems is very important to maintain social stability and prevent unexpected group events and system failure. To monitor passenger flow, data are collected by sensors deployed in important stations and many existing control charts can be applied. However, because of unknown complex distributions and the requirement to detect shifts of all ranges effectively, conventional methods may perform poorly. Nevertheless, while there are certain charting schemes that truncate the Log-Likelihood Ratio (LLR) function to detect large shifts more quickly, they can cause massive loss of information by truncation, and can only handle particular distributions, leading to unstable online monitoring. In this article, we propose a nonparametric CUSUM charting scheme to monitor passenger flow dynamically. We propose a novel minimum distance criterion to minimize the functional distance between the objective function and the original LLR function while maintaining its monotonically increasing property. By integrating this concept with kernel density estimation, our proposed chart does not require any parametric process distribution, it can be constructed easily in any situation, and it is sensitive to shifts of all sizes. Theoretical analysis, simulations and a real application to monitoring passenger flow in the Mass Transit Railway in Hong Kong show that our method performs well in various cases.

Keywords:

• Cumulative sum
• kernel estimation
• minimum distance criterion
• passenger flow monitoring
• robust likelihood ratio

Acknowledgments

The authors thank the editor, the department editor, the associate editor, and the three anonymous referees for their valuable comments and suggestions, which have significantly improved the quality of this paper.

Additional information

Funding

This work was supported by National Key Research and Development Program of China [2021YFA1000101], National Natural Science Foundation of China [11871324; 12071144; 71931004], RGC GRF [16216119], Foshan HKUST Projects [FSUST20-FYTRI03B], National Bureau of Statistics of China [2020LD03], National Science Foundation of Shanghai [19ZR1414400], China Postdoctoral Science Foundation [2020M671064].

Notes on contributors

Yifan Li

Yifan Li received his BS degree in applied mathematics from Xiamen University, China. He is currently working toward a PhD degree in the School of Statistics and Management, Shanghai University of Finance and Economics. His research interests include statistical process control and applied statistics.

Chunjie Wu

Chunjie Wu is a professor and also Vice Dean of School of Statistics and Management, Shanghai University of Finance and Economics. He received both his BS and PhD from the Nankai University. His research interests include statistical process control and applied statistics.

Wendong Li

Wendong Li is an assistant professor in the School of Statistics and Management, Shanghai University of Finance and Economics. He received both his BSc and PhD from East China Normal University. His research interests include statistical process control.

Fugee Tsung

Prof. Fugee Tsung is Chair Professor and Acting Dean of the Information Hub, Guangzhou Campus, at the Hong Kong University of Science and Technology. He is also the Director of the Quality and Data Analytics Lab and former Editor-in-Chief of the Journal of Quality Technology. He has been elected Academician of the International Academy for Quality (IAQ), Fellow of the American Statistical Association (ASA), the Institute of Industrial and Systems Engineers (IISE), the American Society for Quality (ASQ), and the Hong Kong Institution of Engineers (HKIE). He received his PhD and MSc from the University of Michigan, Ann Arbor. He authored over 150 refereed journal publications and received IISE Transactions’ Best Paper Award three times in 2004, 2009, and 2018. His research interests include industrial big data and quality analytics.