# Seismic Reliability Assessment of Water Supply Systems Considering Critical Paths
## 3 Application and Results
### Application Results
#### 3.4.3. Relation between \(S_{s}\) and Pipe Replacement Cost  
A summary of \(S_{s}\), the cost of earthquake-resistant pipes, and the net water inflow of each critical path are shown in Figures 7 and 8 and Table 5. In the RES2 Pipeline, the highest level of system supply can be achieved, but the cost of earthquake resistance is very high, which is a limiting factor when attempting to identify the highest priority pipeline for improvement in consideration of economic efficiency. However, in areas where the risk of large-scale earthquakes is very high, the earthquake resistance of the RES2 Pipeline, which fulfills the largest water supply demand, is essential to maximize the reliability of the water supply regardless of economic factors. The reliability analysis of the water supply for each section does not take into account the relative quantity of water demanded by each route. Therefore, when prioritizing in consideration of the demand for water supply, the RES1 and RES2 Pipelines must be made earthquake resistant. However, since the RES1 and RES2 Pipelines have very long pipes, the two can be divided into sections and a priority can be set for each subsection through an analysis of second- and third-phase relationships and detailed demand sources and a re-evaluation of the seismic reliability of each subsection. If only the rank sum results, which summarize the rank of each indicator, in consideration of both economics and reliability, were used, the RES5 Pipeline could have been chosen as the highest priority for pipeline replacement. However, the RES5 Pipeline occupies a very small proportion of the total system, pipeline length, and demand for water, so the actual effect of seismic reliability improvement in terms of the whole system is small. Therefore, similar to the RES7 and RES8 Pipelines, it is reasonable to deprioritize the RES5 Pipeline because it is composed of small-diameter pipes--even though making it earthquake resistant would be associated with relatively little economic cost--and instead focus on making other pipelines earthquake resistant when doing so would significantly increase the reliability of the system as a whole. Of course, since this study only calculated the cost of earthquake resistance of the pipeline itself, additional analyses that include a replacement timescale, the construction environment, and human resources are needed in order to more accurately determine priorities for pipeline replacement. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Critical Path (Pipeline)** &
\begin{tabular}{c} **Pipeline Replacement Cost (Thousand USD)** \\ **(Earthquake Resistant Ductile Iron Pipe, Suggested by Japan)** \\ \end{tabular} & **Rank** \\ \hline RES1 Pipeline & 10,372 & 8 \\ RES2 Pipeline & 21,039 & 9 \\ RES3 Pipeline & 8176 & 7 \\ RES4 Pipeline & 3327 & 6 \\ RES5 Pipeline & 1893 & 1 \\ RES6 Pipeline & 2695 & 3 \\ RES7 Pipeline & 2748 & 4 \\ RES8 Pipeline & 3142 & 5 \\ RES9 Pipeline & 2166 & 2 \\ Total (Entire System) & 55,558 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Pipeline Replacement Cost by Critical Path. If the rank sum results, which summarize the rank of each indicator, in consideration of economics, reliability, and water quantity demand were used, the RES1, 2, and 8 Pipelines may have been chosen as seismically vulnerable routes. We determined that the RES7 Pipeline, which has a low water quantity demand in comparison to the other pipelines, should be excluded. As such, it seems that it is necessary to consider whether the whole system is in need of seismic reliability improvement. Figure 8: Relationship of System Serviceability (\(S_{s}\)), Cost of Earthquake Resistance, and Supply in Each Critical Path. Figure 7: System Serviceability (\(S_{s}\)) of Each Critical Path vs. Cost of Earthquake Resistance.