A system and method of managing a network with assets are described. The method includes generating a directed graph with each of the assets represented as a node, determining individual failure probability of each node, computing downstream failure probability of each node according to an arrangement of the nodes in the directed graph, computing upstream failure probability of each node according to the arrangement of the nodes in directed graph, and computing network failure probability for each node based on the corresponding individual failure probability, the downstream failure probability, and the upstream failure probability. Managing the network is based on the network failure probability of the assets.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method of managing a network with assets, the method comprising: generating, using a processor, a directed graph with each of the assets represented as a node; determining individual failure probability of each node; computing, using the processor, downstream failure probability of each node according to an arrangement of the nodes in the directed graph; computing, using the processor, upstream failure probability of each node according to the arrangement of the nodes in the directed graph; computing network failure probability for each node based on the corresponding individual failure probability, the downstream failure probability, and the upstream failure probability; and managing the network based on the network failure probability of the assets. 2. The method according to claim 1, further comprising classifying each node in the directed graph. 3. The method according to claim 2, wherein the network is an electric power network and the classifying each node includes classifying each node as a non-protective electrical asset, a protective electrical asset, or a physical asset. 4. The method according to claim 2, wherein the network is a gas pipeline and the classifying each node includes classifying each node as a non-protective asset such as a gas pipe, junction, or pump, a protective asset such as a check valve, or a physical asset such as a pipe section support. 5. The method according to claim 1, wherein the determining the individual failure probability of each node includes extrapolating from a training model that is trained with historical data. 6. The method according to claim 1, wherein the computing the downstream failure probability for each node is based on a classification of one or more assets downstream of the node. 7. The method according to claim 1, wherein the computing the upstream failure probability for each node involves an iterative process. 8. The method according to claim 7, wherein the computing the upstream failure probability for each node is based on the network failure probability of upstream nodes of a modified directed graph that omits the node. 9. The method according to claim 7, wherein the computing the network failure probability for each node is also based on a physical failure probability. 10. The method according to claim 1, wherein the managing the network based on the network failure probability of the assets includes modifying an inspection and maintenance schedule of the assets based on the network failure probability of the assets. 11. The method according to claim 1, wherein the managing the network based on the network failure probability of the assets includes setting a threshold network failure probability and, when the network failure probability of one of the assets exceeds the threshold network failure probability, managing the one of the assets as a critical asset. 12-20. (canceled)