An EWMA control chart for categorical processes with applications to social network monitoring

Abstract

Statistical process monitoring (SPM) has traditionally been applied to manufacturing processes; however, more recent developments highlight its application to social networks. We propose a network monitoring strategy using the exponentially weighted moving average (EWMA) control chart, with the goal of detecting shifts in the hierarchical tendency of directed graphs over time. Such a strategy might prove useful to an organization’s stakeholders when interest lies in monitoring for shifts in the general health of the organization. Although development of the proposed control chart was motivated by a network monitoring problem, our method is generally applicable to multinomial categorical processes. We study the detection performance of our proposed control chart, relative to that of the multinomial cumulative sum (CUSUM) alternative. Results suggest that if the out-of-control shift in the multinomial probabilities cannot be specified a priori, the proposed EWMA control chart should be considered as an alternative to the CUSUM strategy. Application of the proposed method is demonstrated on a real data set, namely, the open-source Enron e-mail corpus.

Keywords:

• directed networks
• EWMA control chart
• hierarchical graph
• multinomial process
• statistical process control
• reciprocity
• transitivity

About the author

Dr. Marcus B. Perry is a Professor of Statistics in the Department of Information Systems, Statistics and Management Science in the Culverhouse College of Commerce at the University of Alabama, Tuscaloosa. He is a member of ASQ and his e-mail address is [email protected]

Acknowledgements

I thank the editor and the two anonymous referees for their constructive comments and suggestions that have considerably improved this article.

Notes

1 https://en.wikipedia.org/wiki/Enron_scandal

2 The specific data set used for this illustration is available from the author upon request.

3 A C++ implementation of a Monte Carlo simulation model of the proposed EWMA control chart is available from the author upon request.

4 https://en.wikipedia.org/wiki/California_electricity_crisis