Robust Online Detection in Serially Correlated Directed Network

With the increasing complexity of the production process, the diversity of data types contributes to the urgency of developing the network monitoring technology. This paper mainly focuses on an online algorithm to detect the serially correlated directed network robustly and sensitively. Firstly, a transition probability matrix is considered here to overcome the double correlation of primary data. Furthermore, since the sum of each row of the transition probability matrix is one, it also standardizes data that facilitates subsequent modeling. Then we extend the spring-length-based method to the multivariate case and propose an adaptive cumulative sum (CUSUM) control chart on the strength of a weighted statistic to monitor directed networks. The novel approach only assumes that the process observation is associated with nearby points without any parametric time series models, which should be coincided with the fact. Simulation results and a real example of metro transportation demonstrate the superiority of our design.