Table 1

Description of the five resilience metrics studied

Resilience metricFormulation
Flow Entropy (FE) (Tanyimboh & Templeman 1993)  Resilience Index (RI) (Todini 2000) Network Resilience Index (NRI) (Prasad & Park 2004)  Modified Resilience Index (MRI) (Jayaram & Srinivasan 2008) Probabilistic Resilience Index (PRI) Resilience metricFormulation
Flow Entropy (FE) (Tanyimboh & Templeman 1993)  Resilience Index (RI) (Todini 2000) Network Resilience Index (NRI) (Prasad & Park 2004)  Modified Resilience Index (MRI) (Jayaram & Srinivasan 2008) Probabilistic Resilience Index (PRI) Parametric description: where n = number of demand nodes; = demand at node j; = head available at node j; = minimum head required to meet constraints at node j; R = number of reservoirs; = flow being supplied to the system by reservoir r; = head at reservoir r; and = power introduced in the system by pump b; = number of pipes connected to node j; = diameter of pipe connected to node j; and = probability of failure of pipe l connected to node j.

For flow entropy: denotes the entropy of the sources (all reservoirs, tanks or external source nodes k R); where n is the number of nodes, where denotes the total flow reaching node i and denotes the entropy of node i, where Q is the sum of nodal demands, where is the inflow from source k, where is the demand at node i, where denotes the set of all the nodes immediately upstream from and connected to node j, and is the flow in the pipe from node i to node j.

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