Large-scale physical networks, such as urban water supply systems, produce failure and maintenance data during the operation, which contain rich system reliability information. Modeling the recurrent failure data on large-scale networks can help to capture failure patterns, plan maintenance program, and ensure high reliability of the system. Considering the temporal and spatial dependence in node failures, we propose a hierarchical modeling method for recurrent failures on large directed networks. We establish a gamma-Poisson autoregressive model on directed networks, and propose a maximum likelihood estimation method based on the sum-product algorithm and the Bethe approximation. This model has been successfully applied to the failure data modeling of a water supply network containing 14910 water pipes. We quantified the influential factors for water pipe failures, and identified high-risk nodes in the water supply network. The results provide management basis for reliable operation of the water supply network.

Qingqing Zhai received the Ph.D. degree in systems engineering from Beihang University, Beijing, China, in 2015. He is currently an Associate Professor with the School of Management, Shanghai University, Shanghai, China. He has authored or coauthored more than 40 articles including JASA, Technometrics, IISE Transactions and IEEE Transactions. His main research interests include degradation modeling, applied statistics, and game theories in reliability.