  As the complexity of production processes increases, the diversity of data
types drives the development of network monitoring technology. This paper
mainly focuses on an online algorithm to detect serially correlated directed
networks robustly and sensitively. First, we consider a transition probability
matrix to resolve the double correlation of primary data. Further, since the
sum of each row of the transition probability matrix is one, it standardizes
the data, facilitating 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. This novel approach assumes only that the process
observation is associated with nearby points without any parametric time series
model, which is in line with reality. Simulation results and a real example
from metro transportation demonstrate the superiority of our design.
