Adachi and Ellingwood  developed the serviceability ratio. The serviceability ratio of WDN is related to the connectivity number of water distribution nodes.
where S represents the serviceability ratio; [omega] is the weight; X is the functionality of the infrastructure; X = 1 indicates that the functionality of the infrastructure is effective; otherwise X = 0; N is the number of nodes in WDN.
(2) Evaluate the serviceability ratio using system reliability.
Figure 6 illustrates the serviceability ratio at each time step under different tolerance parameters ([alpha] = 0.5 and [alpha] = 1.0).
Specific to t = 2 and t = 3, Figure 7 shows the difference on serviceability ratio. In Figure 7, the blue line and the red line represent the serviceability ratio under [alpha] = 0.5 and [alpha] = 1.0, respectively.