Modeling Recurrent Failures on Large Directed Networks

Many lifeline infrastructure systems consist of thousands of components configured in a complex directed network. Disruption of the infrastructure constitutes a recurrent failure process over a directed network. Statistical inference for such network recurrence data is challenging because of the large number of nodes with irregular connections among them. Motivated by 16 years of Scottish Water operation records, we propose a network Gamma-Poisson Autoregressive NHPP (GPAN) model for recurrent failure data from large-scale directed physical networks. The model consists of two layers: the temporal layer applies a Non-Homogeneous Poisson Process (NHPP) with node-specific frailties, and the spatial layer uses a well-orchestrated gamma-Poisson autoregressive scheme to establish correlations among the frailties. Under the network-GPAN model, we develop a sum-product algorithm to compute the marginal distribution for each frailty conditional on the recurrence data. The marginal conditional frailty distributions are useful for predicting future failures based on historical data. In addition, the ability to rapidly compute these marginal distributions allows adoption of an EM type algorithm for estimation. Through a Bethe approximation, the output from the sum-product algorithm is used to compute maximum log-likelihood estimates. Applying the methods to the Scottish Water network, we demonstrate utility in aiding operation management and risk assessment of the water utility.