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Evaluating the performance of water distribution network deterioration using customer-oriented performance indices

Orime, Henry; Tait, Simon; Boxall, Joby; Schellart, Alma; Shepherd, Will

Abstract

Water distribution networks (WDNs) are an essential urban infrastructure, with their performance directly influencing societal well-being. Our study applied to a real network model that employs a 24-h simulation with 1-h time steps and evaluates the impact of leaks and loss in the pipe cross-sectional area on WDN hydraulic performance as experienced by end users. Adhering to a UK utility's 20-m head pressure requirement as the water main benchmark, we present two new customer-oriented performance indices (CPIs) centred on network reliability and pressure deficit severity. The new CPIs adeptly quantify network performance degradation due to pipe deterioration. This degradation translates directly to a poor customer experience, highlighting the potential for these CPIs to pinpoint areas of the network where performance levels are compromised. Furthermore, the CPIs identify individual pipes within the network where defects would severely impact network performance and the sets of pipes which, when simultaneously experiencing defects, would lead to a more severe loss in network performance. Results show that the CPIs capture relatively small performance declines and identify sensitive pipes impacting network performance, providing insights for optimised inspection and maintenance intervention to provide better customer service.

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Evaluating the performance of water distribution network deterioration using customer-oriented performance indices Henry Orime *, S. Tait, J. Boxall, W. Shepherd and A. Schellart Department of Civil and Structural Engineering, The University of Sheffield, Sheffield, UK *Corresponding author. E-mail: hcorime1@sheffield.ac.uk HO, 0009-0008-9108-9819 ABSTRACT Water distribution networks (WDNs) are an essential urban infrastructure, with their performance directly influencing societal well-being. Our study applied to a real network model that employs a 24-h simulation with 1-h time steps and evaluates the impact of leaks and loss in the pipe cross-sectional area on WDN hydraulic performance as experienced by end users. Adhering to a UK utility’s 20-m head pressure requirement as the water main benchmark, we present two new customer-oriented performance indices (CPIs) centred on network reliability and pressure deficit severity. The new CPIs adeptly quantify network performance degradation due to pipe deterioration. This degradation translates directly to a poor customer experience, highlighting the potential for these CPIs to pinpoint areas of the network where performance levels are compromised. Furthermore, the CPIs identify individual pipes within the network where defects would severely impact network performance and the sets of pipes which, when simultaneously experiencing defects, would lead to a more severe loss in network performance. Results show that the CPIs capture relatively small performance declines and identify sensitive pipes impacting network performance, providing insights for optimised inspection and maintenance intervention to provide better customer service. Key words: customer-oriented performance indices, pipe deterioration, pressure deficit, water distribution network HIGHLIGHTS •Novel customer performance indices (CPIs) to evaluate water network’s performance. •The study employs minimum pressure over time requirements as a reflection of customer experience. •Findings show how pipe leaks and cross-sectional area loss in different areas of the network impact customer experience. •CPIs can guide targeted inspections for improved network performance and customer experience. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/). © 2024 The Authors Water Supply Vol 24 No 11, 3759 doi: 10.2166/ws.2024.240 Downloaded from http://iwaponline.com/ws/article-pdf/24/11/3759/1511897/ws2024240.pdf by guest on 12 December 2025 GRAPHICAL ABSTRACT INTRODUCTION Water distribution networks (WDNs) are essential for delivering potable water to urban and rural populations, and their efficient operation is critical to ensuring reliable service and maintaining consumer satisfaction. However, ageing WDNs are susceptible to defects which can significantly impair hydraulic performance, increase operational costs, and diminish customer satisfaction (Boxall et al. 2004;Almandoz et al. 2005; Farley & Trow 2005; Aminu Beshir et al. 2024). To mitigate these challenges and maintain reliable service, utilities must employ effective inspection, maintenance, and rehabilitation strategies, addressing defects that impact hydraulic performance to avoid disruptions (Parvizsedghy et al. 2017;D’Ercole et al. 2018). Incorporating customer-centric variables into performance assessments of water utilities has gained momentum over the past two decades. Since 1999, when water companies in England and Wales introduced the overall performance assessment (OPA) framework, there has been a shift towards evaluating service quality from the consumer’s perspective. Picazo-Tadeo et al. (2008) note that Saal & Parker (2001) were among the first to include customer satisfaction in the performance measurement of water utilities, laying the foundation for more comprehensive frameworks that balance technical efficiency with consumer expectations. Building on this foundation, Sala-Garrido et al. (2021) integrated customer-related performance indicators (PIs), such as service interruptions and complaints, into the ‘benefit of the doubt’composite indicator framework. This approach provides a more holistic evaluation of water service quality, incorporating technical and customer-focused metrics. The WUSQI and the benefit of the doubt indicators effectively assess water utility performance from a customer-centred standpoint by evaluating customer contacts and service interruptions, planned or unplanned. However, they lack the granularity to identify specific issues within the utility’s network. A method that evaluates performance directly from the utility’s network, linking customer satisfaction to hydraulic parameters, would provide valuable insights into utility quality of service. This approach would enhance customer satisfaction by informing proactive decisions for effective network management. In a related study, Mocholi-Arce et al. (2021) emphasised the importance of variables like water leakage and bursts per kilometre as key indicators of water utility productivity. Reducing such incidents enhances operational efficiency and significantly improves customer satisfaction. Furthermore, Duarte et al. (2009) introduced the global index of service quality Water Supply Vol 24 No 11, 3760 Downloaded from http://iwaponline.com/ws/article-pdf/24/11/3759/1511897/ws2024240.pdf by guest on 12 December 2025 (GISEQ), integrating various PIs related to customer satisfaction and service reliability, further demonstrating the industry’s growing recognition of the need for customer-oriented performance assessments. The increasing importance of customer experience to water utilities has led to the demand for more customer-centric approaches for evaluating performance. Assessing the performance of WDNs requires balancing utility-driven objectives such as operational efficiency and equitable water distribution with the needs and expectations of customers, who prioritise affordability, reliable supply, and minimal service interruptions (Naamani & Sana 2021). Traditional PIs for evaluating utility services or their networks are often selected based on ease of calculation, availability of data, or even local traditions rather than their technical suitability for meaningful comparisons across the systems. This approach can produce indicators that merely create a positive impression of performance rather than reflecting the level of service. As a result, important insights into operational inefficiencies may be missed, undermining efforts to improve water management (Cheong 1991). The proper basis for selecting PIs should focus on those that offer the most rational technical basis for comparison, ensuring that performance assessments are accurate and actionable. Similarly, Kwietniewski (2004) models water distribution system (WDS) reliability using a system-wide pressure performance index, focusing on fault states and overall system probabilities. While this highlights the likelihood of events occurring, it overlooks the need for detailed, node-specific analysis, such as how faults in particular pipes or areas of the network impact pressure variations at WDS nodes, directly affecting customer service in the network. To address these challenges, utilities and regulators have consistently developed new performance assessment tools and improved existing performance methodologies to help balance operational goals with customer satisfaction. These tools, used during both the design and operational phases of WDN management, establish benchmarks for supply reliability, pressure management, and overall service quality (Ofwat 2005). Cardoso et al. (2004) identified two primary methods for evaluating water supply system performance: PIs and technical performance assessment. International organisations, such as the International Water Association (IWA), the Office of Water Services (Ofwat), and the International Benchmarking Network (IBNET), have developed specific PIs to measure the reliability of water services provided by utilities quantitatively. These indicators focus on crucial aspects such as the frequency and duration of supply interruptions, pressure levels in distribution systems, leakage rates, and customer complaints (Ofwat 2005;Van den Berg & Danilenko 2010;Alegre et al. 2016). For instance, Ofwat uses metrics like the percentage of customers experiencing supply interruptions lasting more than 3 h, as well as the average duration of interruptions per year. Similarly, IWA has created a set of key performance indicators (KPIs) that assess water loss (using the infrastructure leakage index), supply continuity, and system responsiveness to disruptions. IBNET’s benchmarking framework also includes indicators that measure both physical losses in the system and the responsiveness to customer complaints about service reliability. These standardised PIs provide a clear, data-driven framework that helps utilities benchmark their service quality, identify areas for improvement, and compare their performance with global best practices. Water utilities can ensure they meet regulatory standards by applying these indicators while enhancing service reliability and customer satisfaction. These indicators help benchmark and improve utility service quality but are reactive, averaged for network regions, and lack the granularity to inform pipe-level operations and maintenance within the utility network. Technical performance assessment tools typically focus on system hydraulics, using parameters such as pressure, velocity, and flow rate to evaluate performance. Alegre & Coelho (1995) introduced technical performance indices (TPIs) that assess hydraulic performance based on nodal pressure heads. Other studies, such as those by Todini (2000) and Prasad & Park (2004), have used resilience indices to measure WDN performance, incorporating factors such as nodal demand and hydraulic heads. Yazdani & Jeffrey (2012) proposed a topological performance index to quantify water distribution systems’ redundancy and structural robustness. Tanyimboh & Sheahan (2002) developed an optimised WDN layout using the entropy index to improve WDN performance. Although entropy, topography, and resilience metrics are known to inform WDN design decisions, they are limited mainly by their focus on network connectivity, redundancy, and the ability to restore operation after a disruption without considering the customer experience. While entropy, topography, and resilience metrics ensure alternative flow paths and system recovery, they do not guarantee that the pre-disruption service levels are maintained after the failure event (Knoeri et al. 2016). Consequently, they fall short of evaluating performance from a customer-centric perspective, which requires ensuring that water supply meets demand at the desired service levels consistently. Water Supply Vol 24 No 11, 3761 Downloaded from http://iwaponline.com/ws/article-pdf/24/11/3759/1511897/ws2024240.pdf by guest on 12 December 2025 The growing emphasis on customer-centric performance evaluation offers a more comprehensive perspective on WDN performance. By integrating customer-focused metrics with traditional technical evaluations while maintaining service reliability, utilities can better align system operations with customer expectations. This holistic approach enhances operational efficiency and improves customer satisfaction, particularly in ageing networks prone to service disruptions. In this context, the study introduces a novel approach to evaluating WDN performance by focusing on pipe-level analysis using customer-oriented performance indices (CPIs), prioritising maintaining minimum pressure levels to meet user demand. Unlike broader utility-level assessments, this method allows for identifying specific pipes critical to maintaining network performance. By examining how leaks and reductions in pipe cross-sectional areas impact hydraulic performance, the method pinpoints vulnerable pipes that pose a risk to service quality. This granularity enables utilities to optimise operations and maintenance, allowing for targeted repairs and proactive inspection strategies. Ultimately, this approach mitigates service disruptions, enhances operational efficiency, and ensures reliable water delivery, significantly improving customer satisfaction by addressing issues at their source. METHODS We proposed CPIs that assess service levels using time-series pressure data. The study employed WNTR-EPANET (Rossman 2000;Klise et al. 2017), considering it is open source and has existing Python libraries, which enable efficient implementation of the deterioration scenarios and automate the simulation process. The simulation was performed by setting the demand model to pressure-dependent demand (PDD), which produces realistic hydraulic simulation results during disruptive events in WDNs (Rossman 2000). Nodal pressure time-series results from the simulation are applied to compute the CPIs. Establishing a system-wide pressure threshold is valuable for monitoring network operation and performance. In England and Wales, utilities must maintain a minimum pressure of 10 m while providing 9 litres of water per minute at the customer tap of primary use, according to Ofwat (2005), this is often interpreted as a static pressure of 17 m in the street. Shin et al. (2018) emphasised that increasing system pressure is a common strategy to ensure resilience against hydraulic disruptions, which can significantly enhance the ability of a water distribution system to meet pressure and flow requirements even during disruption. For instance, Yorkshire Water, a water utility in England, often designs its WDNs with 20 m pressure heads. This study adopted Yorkshire Water’s (2020), and common across the UK, minimum water main pressure of 20 m head outside all properties, but other thresholds can be used. Development of proposed CPIs This study simulated a case study network for 24 h with a 15-min timestep, considering the minimum required pressure (P)of 20 m at node jto meet user demand. A CPI of 1.0 for node jindicates that node jreceives pressure higher or equal to the minimum pressure requirement throughout the simulation period. The following conditions for developing the CPIs were introduced in Equation (1): If Pj20 m, CPI ¼1 If Pj,20 m, CPI =1 (1) CPI1measures the WDN’s reliability in meeting the 20-m pressure threshold. CPI1considers the pressure deficits in network nodes throughout the 24-h simulation period. A pressure deficit period is defined as a period during which the pressure at node jgoes below 20 m. The CPI1for node j(denoted as CPI1,j) is calculated as one minus the ratio of the summed duration of all pressure deficit periods at node jto the total simulation time (Ts), this can be written as: CPI1,j¼1P n i¼1 Ti,j Ts (2) CPI2investigates the WDN’s performance based on the severity of pressure deficit over time compared with the 20-m pressure threshold. It measures this severity by considering the area under the curve of pressure deficit over time. CPI2for node j(denoted as CPI2,j) is calculated as one minus the ratio of the summed area of the period of all pressure deficit (Ai,j) at node jto the product of the pressure threshold of 20 m head and the total simulation time (Ts) and denoted as AS. Water Supply Vol 24 No 11, 3762 Downloaded from http://iwaponline.com/ws/article-pdf/24/11/3759/1511897/ws2024240.pdf by guest on 12 December 2025 Where AS¼20Tsserving as a reference area, this can be written as: CPI2, j¼1P n i¼1 Ai,j AS (3) The overall network performance denoted as CPINet is computed as the average CPI of the nodes in the network. This is calculated based on the total number of nodes, N, in the network, as shown in Equation (4): CPINet ¼1 NX N j¼1 CPIj(4) Scenario 1: Impact of 5% leak diameter proportional to pipe diameter In this scenario, the impact of pipe leaks on the WDN performance was assessed using CPIs. Leak sizes of 5% of each pipe’s manufacturer diameter D0were applied based on a study by Yu et al. (2019). The leak diameter Dleak for each pipe was determined using Equation (5) was then used to calculate the leak area in Equation (6). The leak area was normalised as a ratio of the leak area to the original pipe area, as shown in Equation (8). This normalisation process captured the relative change in leak size across varying pipe diameters in the network, allowing for a standardised comparison of leak areas across different pipes and a more comprehensive system performance analysis. Dleak ¼5% D0(5) Aleak ¼ p Dleak 2  2 (6) A0¼ p D0 2  2 (7) Normalised leak area ¼Aleak A0 (8) Leak discharge was modelled using the emitter settings feature in Rossman (2000). The process involved splitting the pipe, creating an artificial node along the pipe, and applying an emitter at that node to simulate a pressure-driven discharge as given in Equation (9): Qleak ¼Kleak P b (9) where Kleak is the emitter coefficient that represents the size of the leak (related to the leak area), Pis the pressure at the leaking node since it is modelled by breaking a pipe length and introducing it at the joint where the leak is applied, and b is the pressure exponent, set to 0.5 in this study, assuming a leak from an orifice as turbulent flow. Scenario 2: Loss in the cross-sectional area of pipes by 80% This scenario considered individual pipes experiencing a loss in cross-sectional area and their respective impact on the network performance based on the CPIs. The reduction in diameter was quantified as an 80% loss in the pipe diameter based on findings from Rathnayaka (2016). Given D0as the original diameter of the pipe, the effective diameter was computed using Equation (10) factoring in the pipe roughness to the deteriorated diameter at 80% was derived from Equation (11). In this scenario, loss of pipe capacity was simulated based on a study by Boxall et al. (2004), which identified reduced pipe diameter and roughness as notable determinants when estimating the impact of deterioration in WDN models. To account for the impact of roughness and pipe diameter reduction, the diameter of pipes in the case study was adjusted using the formula: For original state: Deffective ¼[D02(K0)] (10) Water Supply Vol 24 No 11, 3763 Downloaded from http://iwaponline.com/ws/article-pdf/24/11/3759/1511897/ws2024240.pdf by guest on 12 December 2025 where K0represents the roughness of the pipe in the calibrated case study network and D0is the inner diameter of the pipe. DLoss in diameter ¼80% Deffective (11) The roughness and diameter reduction adjustment were applied selectively to the pipes tested in each simulation cycle, rather than uniformly across the entire network, to provide a precise and localised assessment of hydraulics. Factoring the roughness into the diameter adjustment using Equation (10), the model analysis captured the effect of increased flow resistance caused by pipe surface degradation and the corresponding reduction in cross-sectional area. Performance levels and estimation of proportions nodes operating within each performance level The CPIs are classified into five levels based on the WDN’s ability to maintain the minimum required pressure. 0–0.2 indicates a severe impact, 0.2–0.4 indicates a significant impact, 0.4–0.6 corresponds to a moderate impact, 0.6–0.8 reflects a minor impact, and 0.8–0.999 represents a slight impact. All CPI values under 1 indicate some level of pressure deficit. Furthermore, we used the cumulative distribution function (CDF) methodology to evaluate the CPI distribution across all impact levels and clarify the impact trend at nodes. In this case, the CDF sorted the CPI values at nodes for each pipe or combination, starting from zero, and plots the cumulative proportion of nodes affected. It enabled a clear comparison of how single pipe or their combinations contribute to performance degradation, with the stepwise progression highlighting the extent and range of nodal impacts across the network. Case study water distribution network Figure 1 presents a typical UK DMA (District Meter Area) comprising 175 pipes, with pipe lengths ranging from 0.7 to 165 m and diameters varying between 32 and 200 mm. The hydraulic properties of the network are characterised by Figure 1 |Case study network: pressure at nodes and velocity in pipes at 9:00 AM. Water Supply Vol 24 No 11, 3764 Downloaded from http://iwaponline.com/ws/article-pdf/24/11/3759/1511897/ws2024240.pdf by guest on 12 December 2025 Hazen-Williams C-factors, which span from 44 to 150, reflecting the varied roughness of different pipe materials within the network. This WDN was an operational DMA (subsequently changed due to wide-scale system reconfigurations), making it available for research but representative and, hence, suitable for assessing hydraulic performance under varying operational conditions. Initially, all 167 nodes within the network exhibit a CPI of 1 with pressures higher than 50 m, indicating that the nodes’pressure meets the required 20 m standard throughout the simulation period. The network’s demand patterns demonstrate typical diurnal patterns over 24 h, with distinct peaks during early morning hours, fluctuations throughout midday and evening, and lowest demand at night. This dynamic demand profile is vital for demonstrating the CPI’s ability to capture hydraulic performance changes in the network if defective. RESULTS AND DISCUSSION This section presents the results and discusses how pipe defects impact WDN performance using the proposed CPIs. Initially, individual pipes had either the scenario 1 or scenario 2 defect applied. The network was simulated using the PDD simulation approach to evaluate the impact of individual defects on the network’s performance. The CPIs are analysed with a CDF, heatmap, and scatter plots to assess the distribution of CPIs and the number of nodes impacted with service disruption across the network corresponding to each pipe defect. Furthermore, the overall network performance was assessed, and the pipes were ranked according to their sensitivity to network performance. Pipes selected from this ranking are used to demonstrate the effects of multiple simultaneous defects on WDN performance. Results from scenario 1 Impact of individual pipe leak on WDN performance Figure 2 presents the CDF plots for the CPIs across the network, showing the impact of a 5% leak size proportional to each pipe’s diameter, where each pipe is simulated with a leak one at a time, and this process is repeated for all pipes in the network. The results in Figure 2 reveal that 83 pipes caused at least one node to have severe periods of pressure deficits lasting between 19.2 and 24 h, as represented in the 0–0.2 CPI region of the CDF. The heatmap in Supplementary Appendix A1 provides a visual representation of the network’s sensitive pipes for this defect scenario, resulting in a severe period of pressure deficit with CPI₁values between 0 and 0.2, indicated in red corresponding to the Node IDs. From Supplementary Appendix A2, Pipes 31, 32, and 33 rank as the top three, each affecting 34 nodes with severe periods of pressure deficit, as highlighted by the circled Pipe IDs. This suggests that if any of these pipes experience a 5% leak proportional to their diameter, up to 20% of the network’s nodes could face pressure deficits lasting for 19.2 h or beyond. For instance, Supplementary Appendices A1 and A2 show that Pipe IDs 1–54 caused severe periods of pressure deficits in downstream nodes, mainly those farthest from the water source; considering the network configuration as a branched network, leaks in upstream pipes result in reduced pressure at dependent downstream nodes due to limited alternative supply paths. Figure 2 |Nodal CPI distributions based on 5% leak. Water Supply Vol 24 No 11, 3765 Downloaded from http://iwaponline.com/ws/article-pdf/24/11/3759/1511897/ws2024240.pdf by guest on 12 December 2025 Furthermore, from Supplementary Appendix A2, based on the number of nodes impacted per level of impact, Pipes 26, 28, and 29 come at the top of the ranking for pipes resulting in significant periods of pressure deficits if they experience leakage, and affected 26, 5, and 21 nodes, respectively. This means that for Pipes 26, 28, and 29 to experience a leak of the size considered in this analysis, 15, 13, and 8% of nodes in the network are at risk of significant non-compliance with the performance objective of the study. Therefore, customers served by these nodes would likely experience service disruption between 19.2 and 14.4 h a day. Additionally, the results show that 2–7% of nodes in the network experienced moderate pressure deficits lasting between 9.6 and 14.4 h, with CPI₁values of 0.4–0.6, most notably impacted by Pipes 28, 29, and 139, which affected 11, 7, and 5 nodes, respectively. CPI₁offers comprehensive insight by identifying specific pipes responsible for performance decline by not only evaluating the number of nodes with pressure drops, as in Klise et al. (2017) but also quantifying varying levels of pressure deficit durations across the network. As a normalised index over the entire network operational period, CPI₁enables more detailed comparisons across pipes, providing a clearer understanding of system performance over time. This data-driven approach enhances network management by targeting sensitive pipes and enabling timely interventions, ultimately improving customer service quality. Figure 2 for CPI₂complements the CPI₁analysis by capturing the duration and intensity of pressure deficits. The results indicate that while some pipes may have caused severe period pressure deficits at specific nodes, as demonstrated by CPI₁, CPI₂reveals that the deficits’intensity could be minor or slight. The trend is most evident for Pipe IDs 9–16, where Supplementary Appendix A1 shows that Node IDs 6–9 experienced a severe impact based on CPI₁, but CPI₂ indicates only minor to moderate impacts, suggesting that while the pressure deficit lasted for an extended period, its severity remained low. When these observations are analysed against the Ofwat PI, a limitation in the Ofwat performance standard becomes apparent. The Ofwat (2018) performance measures service interruption as any event where pressure falls below 3 m for more than 3 h at the point where water leaves the water mains and enters the customer’s property. This definition fails to account for prolonged pressure deficits at nodes that maintain pressure equal to or above 3 m and vice versa. Although this may shield utilities from compensation claims under the Guaranteed Standards Scheme (GSS), it ignores customers serviced by Node IDs 5–9 who have faced poor service for 19.2 h, regardless of the intensity of the pressure drop being minor. The problem is compounded when these nodes service critical infrastructures such as hospitals and schools, where even minor pressure reductions over an extended period can have significant consequences. The CPIs in this study bridged the gap by offering a nuanced understanding of network performance, capturing the minor intensity and severe duration deficit events that conventional indicators like Ofwat’s might overlook. Furthermore, the analysis indicates a localised impact across the network, such that most pipes severely impact nodes within their section of the network. This is expected, as the case study network is fully branched, with only one supply route to downstream nodes, meaning that when an upstream pipe fails, nodes relying on this pipe for supply could face service disruption. Nodes severely impacted with lower CPI values signal non-compliance with the study’s performance standards, which would negatively impact customer satisfaction within those nodes. The overview of the results demonstrates the ability of the CPIs to guide decision-making for inspection and maintenance for the case study network by pinpointing sets of pipes, those in the category of Pipes 32, 33, and 36, resulting in widespread, prolonged severe pressure deficit with potential high intensity of pressure. Additionally, the performance grading into different levels can serve as a further guide for prioritising pipe inspection and maintenance, focusing on high-risk pipes that influence the service of critical customers. Overall network performance and ranking pipes in order of their impact Regarding the overall network performance, CPINet across all performance levels, the CPIs of all nodes in the network are averaged for each pipe leak, one at a time, focusing primarily on CPI2,Net, since it factors in both the duration and severity of pressure deficit. Pipes are ranked based on their sensitivity using CPI2,Net. This process provides additional insight into the network-wide performance instead of relying entirely on those pipes impacting the highest number of nodes and causing the most extended period of pressure deficit, which could be biased in some cases, mainly when a pipe impacts more nodes with less severity for an extended period and vice versa. Figure 3 displays that CPI2,Net values ranged between 0.85 and 0.95 across all pipes tested with leak one at a time, indicating performance degradation. The previous analysis for CPI₁showed that when assessing the number of nodes impacted and the Water Supply Vol 24 No 11, 3766 Downloaded from http://iwaponline.com/ws/article-pdf/24/11/3759/1511897/ws2024240.pdf by guest on 12 December 2025 duration of pressure deficits, Pipes 31, 32, and 33 were the top contributors of severe duration pressure deficits. These pipes are located at critical sections of the network and serve as only a supply path from the water source to the downstream nodes in their sections of the network, as shown in Figure 4. However, when evaluated from the perspective of overall network performance using the CPI2,Net, Pipe 36 resulted in lower CPI2,Net than Pipe 31, demonstrating a more widespread severity of pressure deficit across the network for the same leak size. Going forward, in the demonstration of multiple simultaneous defect scenarios, the analysis will consider Pipes 32, 33, and 36, which had the lowest CPI2,Net. Impact of simultaneous multiple leak defects on WDN performance The density plots in Figure 5 show CPI1and CPI2assessment of the impact of simultaneous multiple leaks occurrence in Pipes 32, 33, and 36, identified as the most sensitive to the network’s performance (under the size of leak considered in this study) based on CPI2,Net.Table 1 further demonstrates the proportions of nodes within different performance levels. Figure 3 |Overall network performance CPI Net based on 5% leak diameter to pipe diameter. Figure 4 |Identified pipe locations used in the analysis. Water Supply Vol 24 No 11, 3767 Downloaded from http://iwaponline.com/ws/article-pdf/24/11/3759/1511897/ws2024240.pdf by guest on 12 December 2025 REFERENCES Alegre, H., Coelho, S. T., (1995) Hydraulic performance and rehabilitation strategies. In: Cabrera, E. & Vela, A. F. (eds.) Improving Efficiency and Reliability in Water Distribution Systems. London, UK: Kluwer Academic Press, pp. 85–100. Alegre, H., Baptista, J. 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