Modeling and monitoring unweighted networks with directed interactions

Abstract

Networks have been widely employed to represent interactive relationships among individual units in complex systems such as the Internet of Things. Assignable causes in systems can lead to abrupt increased or decreased frequency of communications within the corresponding network, which allows us to detect such assignable causes by monitoring the communication level of the network. However, existing statistical process control methods for unweighted networks have scarcely incorporated either the network sparsity or the direction of interactions between two network nodes, i.e., dyadic interaction. Regarding this, we establish a matrix-form model to characterize directional dyadic interactions in time-independent unweighted networks. With inactive dyadic interactions excluded, the proposed procedure of parameter estimation achieves higher consistency with less computational cost than its alternative when networks are large-scale and sparse. Using the generalized likelihood ratio test, the work derives two schemes for monitoring directed unweighted networks. The first can be used in general cases whereas the second incorporates a priori shift information to improve change detection efficiency in some cases and estimate the location of a single shifted parameter. Simulation study and a real application are provided to demonstrate the advantages and effectiveness of proposed schemes.

Keywords:

• Dyadic interaction; directed network; process monitoring; generalized likelihood ratio test; statistical process control

Acknowledgments

The authors would like to thank the editors and referees for their many constructive and insightful comments, which have promoted great improvements of this article.

Additional information

Funding

The work described in this article was supported by grants from Fundamental Research Funds for the Central Universities, Zhongnan University of Economics and Law (2722019JCG053), Research Grant Council of Hong Kong (CityU 11203519 and CityU 11213116) and also by National Natural Science Foundation of China under a Key Project (71532008).

Notes on contributors

Junjie Wang

Junjie Wang is a lecturer with School of Business Administration, Zhongnan University of Economics and Law. He received the Bachelor’s degree in engineering management from China University of Geosciences, Wuhan. He also obtained two Ph.D. degrees respectively in systems engineering and engineering management from City University of Hong Kong and in management science and engineering from Xi’an Jiaotong University in 2018 under the joint Ph.D. program. His research interests include statistical process control and big data analytics.

Min Xie

Min Xie is a Chair Professor in industrial engineering at City University of Hong Kong. He received his Ph.D. from Linkoping University, Sweden in 1987. He did his undergraduate study and received a M.S. at Royal Institute of Technology in Sweden in 1984. Dr. Xie joined the National University of Singapore in 1991 as one of the first recipients of the prestigious Lee Kuan Yew Research Fellowship. He has authored or co-authored numerous refereed journal papers and several books. He is a Department Editor of IISE Transactions and Editor of Reliability Engineering & System Safety and serves in a number of other international journals. He has organized many international conferences, and also over 50 Ph.D. students have graduated under his supervision. He was elected a fellow of IEEE for his contribution to systems and software reliability.