Resource-Oriented Prioritisation of Water-Supply Pipe Groups Using Repair and Service-Interruption Burdens
Abstract
1. Introduction
- Audit all source records and report outcome-specific denominators;
- Assess temporal comparability, network exposure and repair-time heaping;
- Compare statistically defined pipe, material, diameter and cause groups;
- Evaluate criterion dependence and ranking sensitivity;
- Quantify priority uncertainty and temporal stability.
2. Literature Review
2.1. Pipe Failure, Criticality and Rehabilitation
2.2. Repair Duration and Service Interruption
2.3. Multi-Criteria Prioritisation and Uncertainty
3. Materials and Methods
3.1. Study Area
3.2. Source Records
3.3. Technical Classification and Temporal Comparability
3.4. Variables and Descriptive Analyses
3.5. Operational Indicators
3.6. CRITIC–TOPSIS Models
3.7. Uncertainty, Sensitivity and Adjusted Modelling
- Interruption representation through positive-only SIT;
- Criterion structure;
- Repair threshold (>8, ≥8, >10 and >12 h);
- Minimum group size (10, 20, 30 and 50 events);
- The same three analysis subperiods used for descriptive comparison.
4. Results
4.1. Data Completeness and Network Evolution
4.2. Temporal Patterns
4.3. Repair-Time Distribution and Group Differences
4.4. Adjusted Repair and Interruption Models
4.5. Criterion Dependence and Point Rankings
4.6. Bootstrap Uncertainty and Sensitivity
5. Discussion
5.1. Interpretation of the Ranking
5.2. Relation to Existing Rehabilitation Research
5.3. Operational Use
- Recalculate annual and rolling material–function indicators with outcome-specific denominators and automated data-quality flags.
- Review the leading groups for denominator anomalies, repeated addresses, coding errors and concentration in a small number of segments.
- For verified segments, add age, condition, break history, pressure, valve isolation, customers and critical facilities affected, water not supplied and traffic/access consequences.
- Compare feasible interventions using life-cycle cost, hydraulic benefit, regulatory constraints and coordinated street works.
- Record the decision and subsequent performance so that the screening model can be recalibrated.
5.4. Resource-Management Implications and Transferability
5.5. Limitations
6. Conclusions
- The audited 2004–2025 record retained 4885 events, with separate valid denominators for repair (4859), service interruption (4832) and material (4824). Network length rose by 480 km, while annual failure rate fell from 0.539 to 0.150 failures/(km·year). Annual MTTR showed no significant monotonic trend (ρ = 0.264; p = 0.236), whereas mean SIT increased over time (ρ = 0.560; p = 0.007) and was highest in 2018–2025 (3.44 h). Because network configuration changed, this was an operational signal rather than proof of deteriorating customer service.
- Repair time was strongly heaped: 91.5% of values were whole hours and 64.2% equalled 8 h. The sharp contrast between >8 h (10.8%) and ≥8 h (75.0%) means that repair-threshold results should be treated as sensitivity evidence rather than a natural risk boundary.
- The primary ranking used only failure rate, MTTR and SIT. Galvanised-steel service connections ranked first (CC = 0.819), with P(rank 1) = 0.800 in the event-level bootstrap and 0.684 in the calendar-year block bootstrap; they remained in the block bootstrap top three in every replicate. They also led all minimum-size variants and the positive-only SIT model, but not every subperiod. AC distribution pipes led all product-containing structures and the strict >8, >10 and >12 h threshold variants, whereas the inclusive ≥8 h variant retained galvanised-steel service connections; derived RBI and SIBI should not be added to their own components as independent evidence.
- The result is a relative group-level screening signal, not a renewal prescription. Segment selection still requires hydraulic consequence, users and critical facilities affected, age, condition, isolation, access and life-cycle cost; environmental and socioeconomic benefits can be evaluated only after those dimensions are added. Cause-specific failure rates further support differentiated maintenance: leaky-socket failures dominate mains, corrosion dominates service connections, and the two mechanisms are nearly equal in distribution pipes.
- Beyond the local ranking, this study provides a transferable workflow linking failure occurrence, maintenance burden and water-service accessibility with infrastructure resource allocation. The approach can support utilities in directing limited inspection, repair and renewal resources toward pipe groups generating recurrent operational burdens, while subsequent segment-level decisions should incorporate hydraulic consequences, customers affected, condition, life-cycle cost and, where available, water-loss, energy and environmental indicators.
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
| AC | Asbestos cement |
| CI | Confidence interval |
| CRITIC | Criteria Importance Through Intercriteria Correlation |
| DP | Distribution pipe |
| HC3 | Heteroscedasticity-consistent covariance estimator |
| IQR | Interquartile range |
| M | Mains |
| MCDA | Multi-criteria decision analysis |
| OR | Odds ratio |
| PE | Polyethylene |
| PVC | Polyvinyl chloride |
| S | Service connection |
| TOPSIS | Technique for Order Preference by Similarity to Ideal Solution |
| g | Pipe-group index |
| i | Event or alternative index, according to context |
| j, k | Criterion indices |
| t | Calendar year |
| q | Number of criteria |
| ng | Occurrence count in pipe group g |
| ng,r | Valid repair-duration count in group g |
| ng,s | Valid service-interruption count in group g |
| Lg,t | Length of group g in year t, km |
| Trepair,g,i | Repair duration for event i in group g, h |
| TSI,g,i | Service-interruption duration for event i in group g, h |
| λg | Exposure-normalised failure rate, failures/(km·year) |
| MTTRg | Mean repair duration, h |
| SITg | Mean service-interruption time, h |
| RBIg | Repair Burden Index, h/(km·year) |
| SIBIg | Service-Interruption Burden Index, h/(km·year) |
| τ | Repair-duration threshold, h |
| P(Trepair > τ) | Proportion of valid repairs above threshold τ |
| Cj | CRITIC information quantity for criterion j |
| σj | Scaled standard deviation of criterion j |
| ρjk | Pearson correlation between criteria j and k |
| wj | Normalised CRITIC weight of criterion j |
| Di± | TOPSIS distance from the positive/negative ideal |
| CCi | TOPSIS closeness coefficient for alternative i |
| m | Number of alternatives |
| xij | Original value of criterion j for alternative i |
| rij | Vector-normalised value of criterion j for alternative i |
| vij | Weighted normalised value of criterion j for alternative i |
| Aj± | Coordinate j of the positive/negative TOPSIS ideal profile |
Appendix A
Appendix A.1. Diameter and Failure-Cause Outcomes
| Dimension | Group | nrepair | Repair Mean ± SD (h) | 95% CI Mean (h) | Repair Median (Q1–Q3), h | nSIT | SIT Mean ± SD (h) | 95% CI Mean (h) | SIT Median (Q1–Q3), h |
|---|---|---|---|---|---|---|---|---|---|
| Diameter | ≤63 | 1875 | 7.59 ± 2.16 | 7.48–7.69 | 8.00 (7.00–8.00) | 1865 | 2.52 ± 1.94 | 2.44–2.61 | 2.00 (2.00–3.00) |
| Diameter | (63–100] | 637 | 7.70 ± 2.35 | 7.52–7.89 | 8.00 (7.00–8.00) | 636 | 2.69 ± 2.02 | 2.54–2.84 | 2.50 (2.00–3.50) |
| Diameter | (100–200] | 1385 | 7.93 ± 2.61 | 7.80–8.07 | 8.00 (7.00–8.00) | 1374 | 2.55 ± 2.38 | 2.43–2.68 | 2.50 (1.00–3.50) |
| Diameter | (200–250] | 306 | 8.34 ± 2.77 | 8.04–8.67 | 8.00 (8.00–8.00) | 304 | 2.40 ± 2.82 | 2.10–2.72 | 2.00 (0.00–3.08) |
| Diameter | >250 | 648 | 9.14 ± 3.27 | 8.87–9.40 | 8.00 (8.00–8.00) | 645 | 1.69 ± 2.63 | 1.49–1.90 | 0.00 (0.00–3.00) |
| Cause | Corrosion | 2254 | 7.91 ± 2.50 | 7.81–8.01 | 8.00 (8.00–8.00) | 2243 | 2.48 ± 2.03 | 2.39–2.56 | 2.00 (1.50–3.00) |
| Cause | Leaky socket | 1108 | 8.16 ± 2.74 | 7.99–8.32 | 8.00 (7.38–8.00) | 1106 | 1.50 ± 2.19 | 1.37–1.63 | 0.00 (0.00–2.50) |
| Cause | Loss of tightness | 621 | 8.05 ± 2.40 | 7.87–8.24 | 8.00 (8.00–8.00) | 616 | 2.80 ± 2.23 | 2.63–2.98 | 3.00 (2.00–4.00) |
| Cause | Crack | 259 | 7.71 ± 2.44 | 7.43–8.01 | 8.00 (7.00–8.00) | 257 | 2.91 ± 1.90 | 2.69–3.15 | 2.83 (2.00–3.50) |
| Cause | Mechanical damage | 21 | 6.38 ± 2.23 | 5.45–7.31 | 6.00 (5.00–8.00) | 21 | 2.67 ± 1.42 | 2.08–3.32 | 2.67 (2.00–3.00) |
| Cause | Other/unclear | 596 | 7.84 ± 2.76 | 7.61–8.05 | 8.00 (7.00–8.00) | 589 | 3.28 ± 2.48 | 3.09–3.50 | 3.00 (2.00–4.00) |
| Dimension | Outcome | Groups | H | p |
|---|---|---|---|---|
| Pipe function | Repair | 3 | 113.28 | <0.001 |
| Pipe function | Service interruption | 3 | 200.47 | <0.001 |
| Material (2004–2025) | Repair | 6 | 34.42 | <0.001 |
| Material (2004–2025) | Service interruption | 6 | 179.50 | <0.001 |
| Diameter class | Repair | 5 | 122.87 | <0.001 |
| Diameter class | Service interruption | 5 | 217.39 | <0.001 |
| Failure cause | Repair | 6 | 19.08 | 0.002 |
| Failure cause | Service interruption | 6 | 526.84 | <0.001 |
Appendix A.2. Adjusted Two-Part Service-Interruption Model
| Model Part | Term | Effect | 95% HC3 CI | p |
|---|---|---|---|---|
| Occurrence OR | Year (per year) | 1.107 | 1.092–1.123 | <0.001 |
| Occurrence OR | log(diameter/100 mm) | 0.469 | 0.358–0.616 | <0.001 |
| Occurrence OR | Material: PVC | 2.476 | 1.353–4.531 | 0.003 |
| Occurrence OR | Material: Cast iron | 1.650 | 0.980–2.778 | 0.060 |
| Occurrence OR | Material: Steel | 0.931 | 0.524–1.655 | 0.807 |
| Occurrence OR | Material: Galvanised steel | 1.179 | 0.640–2.173 | 0.598 |
| Occurrence OR | Material: AC | 1.682 | 0.386–7.330 | 0.489 |
| Occurrence OR | Function: Service connections | 0.792 | 0.546–1.148 | 0.219 |
| Occurrence OR | Function: Mains | 0.898 | 0.615–1.313 | 0.581 |
| Occurrence OR | Cause: Leaky socket | 0.203 | 0.140–0.296 | <0.001 |
| Occurrence OR | Cause: Loss of tightness | 0.882 | 0.520–1.499 | 0.643 |
| Occurrence OR | Cause: Crack | 2.823 | 1.406–5.668 | 0.004 |
| Occurrence OR | Cause: Other/unclear | 3.483 | 2.115–5.738 | <0.001 |
| Positive-duration ratio | Year (per year) | 1.009 | 1.006–1.012 | <0.001 |
| Positive-duration ratio | log(diameter/100 mm) | 1.153 | 1.087–1.223 | <0.001 |
| Positive-duration ratio | Material: PVC | 1.071 | 0.993–1.154 | 0.075 |
| Positive-duration ratio | Material: Cast iron | 1.118 | 1.018–1.228 | 0.020 |
| Positive-duration ratio | Material: Steel | 0.981 | 0.882–1.089 | 0.714 |
| Positive-duration ratio | Material: Galvanised steel | 1.174 | 1.054–1.308 | 0.004 |
| Positive-duration ratio | Material: AC | 1.302 | 1.098–1.544 | 0.002 |
| Positive-duration ratio | Function: Service connections | 1.007 | 0.935–1.084 | 0.853 |
| Positive-duration ratio | Function: Mains | 0.905 | 0.810–1.011 | 0.078 |
| Positive-duration ratio | Cause: Leaky socket | 0.891 | 0.818–0.971 | 0.008 |
| Positive-duration ratio | Cause: Loss of tightness | 1.063 | 0.957–1.181 | 0.256 |
| Positive-duration ratio | Cause: Crack | 1.027 | 0.928–1.137 | 0.603 |
| Positive-duration ratio | Cause: Other/unclear | 1.052 | 0.974–1.136 | 0.200 |
Appendix A.3. Complete TOPSIS Calculation
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| Stage | n |
|---|---|
| Numbered source events | 4885 |
| Repair duration calculable | 4859 |
| Service-interruption status/duration calculable | 4832 |
| Explicit ‘no shut-off’ | 1039 |
| All numerical zero interruptions | 1044 |
| Unique material identified | 4824 |
| Pipe function classified | 4876 |
| Unique material and pipe function | 4817 |
| Primary MCDM set | 4806 in 14 groups |
| Subperiods | Events | Exposure (km·yr) | λ (Failures/(km·year) | nrepair | MTTR (h) | Median (IQR) Repair (h) | nSIT | Mean SIT (h) |
|---|---|---|---|---|---|---|---|---|
| 2004–2010 | 1718 | 4444.58 | 0.387 | 1693 | 7.61 | 8.00 (2.00) | 1673 | 2.41 |
| 2011–2017 | 1797 | 5597.72 | 0.321 | 1796 | 8.21 | 8.00 (0.00) | 1791 | 1.68 |
| 2018–2025 | 1370 | 8015.02 | 0.171 | 1370 | 8.06 | 8.00 (0.00) | 1368 | 3.44 |
| Year | Repair Duration | Service Interruption | ||
|---|---|---|---|---|
| Mean Repair Duration, MTTR (h) | 95% Bootstrap CI (h) | Mean Service-Interruption Duration (h) | 95% Bootstrap CI (h) | |
| 2004 | 6.75 | 6.39–7.11 | 2.99 | 2.68–3.34 |
| 2005 | 7.60 | 7.08–8.15 | 3.22 | 2.65–3.82 |
| 2006 | 7.34 | 7.02–7.70 | 1.95 | 1.68–2.22 |
| 2007 | 7.86 | 7.55–8.19 | 2.14 | 1.88–2.40 |
| 2008 | 7.73 | 7.52–7.95 | 2.35 | 2.16–2.54 |
| 2009 | 8.18 | 7.92–8.47 | 2.13 | 1.86–2.42 |
| 2010 | 8.17 | 7.96–8.40 | 2.06 | 1.86–2.28 |
| 2011 | 8.24 | 7.99–8.49 | 1.39 | 1.21–1.62 |
| 2012 | 8.21 | 7.93–8.49 | 1.40 | 1.25–1.54 |
| 2013 | 8.47 | 8.18–8.77 | 1.55 | 1.40–1.71 |
| 2014 | 8.14 | 7.81–8.47 | 1.62 | 1.41–1.84 |
| 2015 | 8.03 | 7.76–8.31 | 1.58 | 1.40–1.77 |
| 2016 | 8.02 | 7.73–8.33 | 2.36 | 2.13–2.63 |
| 2017 | 8.37 | 8.03–8.73 | 2.04 | 1.74–2.36 |
| 2018 | 8.29 | 7.91–8.69 | 2.97 | 2.64–3.31 |
| 2019 | 8.28 | 7.95–8.62 | 3.56 | 3.26–3.89 |
| 2020 | 8.09 | 7.67–8.52 | 3.49 | 3.22–3.76 |
| 2021 | 7.53 | 7.20–7.86 | 3.24 | 3.00–3.49 |
| 2022 | 8.00 | 7.61–8.41 | 3.85 | 3.59–4.13 |
| 2023 | 8.09 | 7.79–8.40 | 3.24 | 2.95–3.53 |
| 2024 | 7.85 | 7.53–8.17 | 3.42 | 3.17–3.70 |
| 2025 | 8.18 | 7.80–8.59 | 3.89 | 3.57–4.22 |
| Dimension | Group | Repair Duration | Service Interruption | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Nrepair | Mean (h) | SD (h) | 95% CI (h) | Median (h) | Q1–Q3 (h) | nSIT | Mean (h) | SD (h) | 95% CI (h) | Median (h) | Q1–Q3 (h) | ||
| Function | Mains | 648 | 9.14 | 3.27 | 8.87–9.40 | 8.00 | 8.00–8.00 | 645 | 1.69 | 2.63 | 1.49–1.90 | 0.00 | 0.00–3.00 |
| Function | Distribution pipes | 2328 | 7.92 | 2.57 | 7.82–8.03 | 8.00 | 7.00–8.00 | 2314 | 2.57 | 2.36 | 2.48–2.67 | 2.50 | 1.00–3.50 |
| Function | Service connections | 1875 | 7.59 | 2.16 | 7.48–7.69 | 8.00 | 7.00–8.00 | 1865 | 2.52 | 1.94 | 2.44–2.61 | 2.00 | 2.00–3.00 |
| Material | Cast iron | 1868 | 8.17 | 2.79 | 8.04–8.30 | 8.00 | 7.50–8.00 | 1852 | 2.21 | 2.47 | 2.10–2.33 | 2.00 | 0.00–3.00 |
| Material | Steel | 1174 | 8.05 | 2.60 | 7.90–8.21 | 8.00 | 8.00–8.00 | 1170 | 2.19 | 1.92 | 2.08–2.30 | 2.00 | 1.00–3.00 |
| Material | Galvanised steel | 881 | 7.57 | 2.26 | 7.42–7.73 | 8.00 | 6.50–8.00 | 875 | 2.78 | 2.33 | 2.63–2.93 | 2.50 | 2.00–3.00 |
| Material | PVC | 305 | 7.72 | 2.44 | 7.44–8.00 | 8.00 | 7.00–8.00 | 303 | 3.13 | 2.30 | 2.88–3.41 | 3.00 | 2.00–4.00 |
| Material | PE | 523 | 7.64 | 2.06 | 7.47–7.81 | 8.00 | 8.00–8.00 | 524 | 2.61 | 1.84 | 2.46–2.76 | 2.50 | 2.00–3.50 |
| Material | AC | 47 | 8.47 | 3.16 | 7.63–9.33 | 8.00 | 7.00–8.00 | 47 | 3.66 | 2.11 | 3.07–4.28 | 3.00 | 2.00–5.00 |
| Failure Cause | Mains n; λ | Distribution Pipes n; λ | Service Connections n; λ | Classified Total n; Pooled λ | Unknown Function n | All Events n |
|---|---|---|---|---|---|---|
| Corrosion | 144; 0.0758 | 676; 0.0715 | 1438; 0.2206 | 2258; 0.1263 | 3 | 2261 |
| Leaky socket | 420; 0.2210 | 674; 0.0712 | 15; 0.0023 | 1109; 0.0620 | 6 | 1115 |
| Loss of tightness | 72; 0.0379 | 312; 0.0330 | 246; 0.0377 | 630; 0.0352 | 0 | 630 |
| Crack | 8; 0.0042 | 144; 0.0152 | 107; 0.0164 | 259; 0.0145 | 0 | 259 |
| Mechanical damage | 1; 0.0005 | 12; 0.0013 | 8; 0.0012 | 21; 0.0012 | 0 | 21 |
| Other/unclear | 11; 0.0058 | 523; 0.0553 | 65; 0.0100 | 599; 0.0335 | 0 | 599 |
| Total | 656; 0.3453 | 2341; 0.2475 | 1879; 0.2882 | 4876; 0.2727 | 9 | 4885 |
| Term | Multiplicative Effect | 95% HC3 CI | p |
|---|---|---|---|
| Year (per year) | 1.006 | 1.005–1.008 | <0.001 |
| log(diameter/100 mm) | 1.072 | 1.038–1.107 | <0.001 |
| Material: PVC | 1.024 | 0.979–1.071 | 0.299 |
| Material: Cast iron | 1.112 | 1.056–1.170 | <0.001 |
| Material: Steel | 1.087 | 1.023–1.155 | 0.007 |
| Material: Galvanised steel | 1.061 | 0.998–1.129 | 0.057 |
| Material: AC | 1.145 | 1.025–1.278 | 0.017 |
| Function: Service connections | 1.046 | 1.001–1.091 | 0.043 |
| Function: Mains | 1.063 | 1.014–1.115 | 0.011 |
| Cause: Leaky socket | 0.944 | 0.904–0.985 | 0.008 |
| Cause: Loss of tightness | 1.036 | 0.978–1.096 | 0.229 |
| Cause: Crack | 1.011 | 0.951–1.074 | 0.729 |
| Cause: Other/unclear | 0.959 | 0.914–1.006 | 0.084 |
| Group | n (all/r/SIT) | Exposure (km·yr) | λ km−1·yr−1 | MTTR (h) | SIT (h) | P(>8 h) | RBI h/(km·yr) | SIBI h/(km·yr) | Core CC | Rank |
|---|---|---|---|---|---|---|---|---|---|---|
| S–galvanised steel | 849 (848/842) | 483.12 | 1.757 | 7.58 | 2.77 | 0.071 | 13.32 | 4.86 | 0.819 | 1 |
| DP–steel | 460 (459/459) | 293.17 | 1.569 | 7.92 | 2.35 | 0.107 | 12.43 | 3.69 | 0.757 | 2 |
| DP–AC | 44 (44/44) | 35.86 | 1.227 | 8.50 | 3.86 | 0.227 | 10.43 | 4.74 | 0.708 | 3 |
| DP–galvanised steel | 29 (29/29) | 22.90 | 1.266 | 7.14 | 3.21 | 0.103 | 9.04 | 4.06 | 0.683 | 4 |
| DP–cast iron | 1381 (1371/1357) | 1696.08 | 0.814 | 7.92 | 2.43 | 0.112 | 6.45 | 1.98 | 0.437 | 5 |
| S–cast iron | 29 (27/26) | 44.22 | 0.656 | 7.57 | 2.19 | 0.074 | 4.97 | 1.44 | 0.343 | 6 |
| M–cast iron | 472 (466/465) | 802.56 | 0.588 | 8.93 | 1.59 | 0.217 | 5.25 | 0.94 | 0.305 | 7 |
| DP–PVC | 219 (219/218) | 3646.05 | 0.060 | 7.76 | 3.26 | 0.087 | 0.47 | 0.20 | 0.207 | 8 |
| M–PE | 37 (37/37) | 403.48 | 0.092 | 9.05 | 2.68 | 0.243 | 0.83 | 0.25 | 0.177 | 9 |
| M–steel | 130 (128/126) | 581.79 | 0.223 | 9.84 | 1.66 | 0.328 | 2.20 | 0.37 | 0.176 | 10 |
| DP–PE | 169 (168/169) | 3736.68 | 0.045 | 7.94 | 2.83 | 0.101 | 0.36 | 0.13 | 0.164 | 11 |
| S–PVC | 80 (80/79) | 533.80 | 0.150 | 7.47 | 2.69 | 0.063 | 1.12 | 0.40 | 0.159 | 12 |
| S–PE | 318 (318/318) | 2073.26 | 0.153 | 7.32 | 2.49 | 0.031 | 1.12 | 0.38 | 0.136 | 13 |
| S–steel | 589 (587/585) | 3339.37 | 0.176 | 7.76 | 2.18 | 0.053 | 1.37 | 0.38 | 0.115 | 14 |
| Criterion | Scaled σj | Conflict Σ(1 − ρjk) | Information Cj | Point Weight | Bootstrap Median Weight (95% Interval) |
|---|---|---|---|---|---|
| λ | 0.340 | 1.985 | 0.674 | 0.347 | 0.355 (0.314–0.407) |
| MTTR | 0.272 | 2.611 | 0.710 | 0.366 | 0.356 (0.311–0.403) |
| SIT | 0.258 | 2.157 | 0.557 | 0.287 | 0.287 (0.247–0.329) |
| Criterion | λ | MTTR | SIT | P(T > 8) | RBI | SIBI | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| λ | 1.00 | −0.22 | 0.23 | −0.06 | 1.00 | 0.96 | ||||||||
| MTTR | −0.22 | 1.00 | −0.39 | 0.94 | −0.16 | −0.23 | ||||||||
| SIT | 0.23 | −0.39 | 1.00 | −0.19 | 0.22 | 0.45 | ||||||||
| P(T > 8) | −0.06 | 0.94 | −0.19 | 1.00 | −0.00 | −0.03 | ||||||||
| RBI | 1.00 | −0.16 | 0.22 | −0.00 | 1.00 | 0.96 | ||||||||
| SIBI | 0.96 | −0.23 | 0.45 | −0.03 | 0.96 | 1.00 | ||||||||
| where | ||||||||||||||
| Value | 1.00 | 0.75 | 0.50 | 0.25 | 0.00 | −0.25 | −0.50 | −0.75 | −1.00 | |||||
| Colour | ||||||||||||||
| Pipe Group | Core | Positive-SIT Core | Threshold-Augmented | Burden | Full | No RBI | No SIBI | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| S–galvanised steel | 1 | 1 | 2 | 3 | 2 | 2 | 2 | ||||||||||||||
| DP–steel | 2 | 2 | 3 | 4 | 3 | 3 | 3 | ||||||||||||||
| DP-AC | 3 | 4 | 1 | 1 | 1 | 1 | 1 | ||||||||||||||
| DP–galvanised steel | 4 | 3 | 4 | 5 | 4 | 4 | 4 | ||||||||||||||
| DP–cast iron | 5 | 5 | 5 | 8 | 7 | 6 | 7 | ||||||||||||||
| S–cast iron | 6 | 6 | 9 | 9 | 9 | 9 | 9 | ||||||||||||||
| M–cast iron | 7 | 7 | 7 | 6 | 6 | 7 | 6 | ||||||||||||||
| DP-PVC | 8 | 10 | 10 | 11 | 10 | 10 | 10 | ||||||||||||||
| M-PE | 9 | 9 | 8 | 7 | 8 | 8 | 8 | ||||||||||||||
| M–steel | 10 | 8 | 6 | 2 | 5 | 5 | 5 | ||||||||||||||
| DP-PE | 11 | 13 | 11 | 10 | 11 | 11 | 11 | ||||||||||||||
| S-PVC | 12 | 14 | 12 | 12 | 12 | 12 | 12 | ||||||||||||||
| S-PE | 13 | 12 | 13 | 14 | 13 | 13 | 13 | ||||||||||||||
| S–steel | 14 | 11 | 14 | 13 | 14 | 14 | 14 | ||||||||||||||
| where | |||||||||||||||||||||
| Rank | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | |||||||
| Colour | |||||||||||||||||||||
| Group | Observed CC | Bootstrap Median CC | 95% Bootstrap CC | Median Rank (95% Interval) | P(Rank 1) | P(Top 3) |
|---|---|---|---|---|---|---|
| S–galvanised steel | 0.819 | 0.819 | 0.770–0.866 | 1.0 (1.0–2.0) | 0.800 | 1.000 |
| DP–steel | 0.757 | 0.755 | 0.691–0.814 | 2.0 (2.0–4.0) | 0.001 | 0.922 |
| DP–AC | 0.708 | 0.700 | 0.528–0.891 | 3.0 (1.0–4.0) | 0.138 | 0.603 |
| DP–galvanised steel | 0.683 | 0.679 | 0.467–0.843 | 4.0 (1.0–4.0) | 0.062 | 0.475 |
| DP–cast iron | 0.437 | 0.438 | 0.403–0.475 | 5.0 (5.0–6.0) | – | – |
| S–cast iron | 0.343 | 0.344 | 0.221–0.478 | 6.0 (5.0–8.0) | – | 0.001 |
| M–cast iron | 0.305 | 0.306 | 0.273–0.341 | 7.0 (6.0–7.0) | – | – |
| DP–PVC | 0.207 | 0.212 | 0.157–0.266 | 8.0 (8.0–10.0) | – | – |
| M–PE | 0.177 | 0.185 | 0.110–0.254 | 10.0 (8.0–14.0) | – | – |
| M–steel | 0.176 | 0.178 | 0.149–0.209 | 10.0 (8.0–13.0) | – | – |
| DP–PE | 0.164 | 0.169 | 0.118–0.229 | 11.0 (8.0–13.0) | – | – |
| S–PVC | 0.159 | 0.165 | 0.117–0.223 | 11.0 (9.0–13.0) | – | – |
| S–PE | 0.136 | 0.142 | 0.106–0.186 | 13.0 (11.0–14.0) | – | – |
| S–steel | 0.115 | 0.123 | 0.095–0.161 | 14.0 (13.0–14.0) | – | – |
| Sensitivity | Specification | Top Group | Rank Correlation | Maximum Change/Note |
|---|---|---|---|---|
| Criterion structure | Core | S–galvanised steel | 1.000 | 0 |
| Criterion structure | Positive-SIT core | S–galvanised steel | 0.938 | 3 |
| Criterion structure | Threshold-augmented | DP–AC | 0.921 | 4 |
| Criterion structure | Burden | DP–AC | 0.754 | 8 |
| Criterion structure | Full | DP–AC | 0.890 | 5 |
| Criterion structure | No RBI | DP–AC | 0.899 | 5 |
| Criterion structure | No SIBI | DP–AC | 0.890 | 5 |
| Repair threshold | >8 h | DP–AC | 1.000 | 0 |
| Repair threshold | ≥8 h | S–galvanised steel | 0.921 | 4 |
| Repair threshold | >10 h | DP–AC | 0.982 | 2 |
| Repair threshold | >12 h | DP–AC | 0.982 | 2 |
| Minimum group n | n ≥ 10 | S–galvanised steel | — | 14 alternatives |
| Minimum group n | n ≥ 20 | S–galvanised steel | — | 14 alternatives |
| Minimum group n | n ≥ 30 | S–galvanised steel | — | 12 alternatives |
| Minimum group n | n ≥ 50 | S–galvanised steel | — | 10 alternatives |
| Subperiod | 2004–2010 | S–galvanised steel | 0.818 | 4 |
| Subperiod | 2011–2017 | DP–AC | 0.727 | 5 |
| Subperiod | 2018–2025 | S–galvanised steel | 0.927 | 3 |
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Pietrucha-Urbanik, K. Resource-Oriented Prioritisation of Water-Supply Pipe Groups Using Repair and Service-Interruption Burdens. Resources 2026, 15, 114. https://doi.org/10.3390/resources15090114
Pietrucha-Urbanik K. Resource-Oriented Prioritisation of Water-Supply Pipe Groups Using Repair and Service-Interruption Burdens. Resources. 2026; 15(9):114. https://doi.org/10.3390/resources15090114
Chicago/Turabian StylePietrucha-Urbanik, Katarzyna. 2026. "Resource-Oriented Prioritisation of Water-Supply Pipe Groups Using Repair and Service-Interruption Burdens" Resources 15, no. 9: 114. https://doi.org/10.3390/resources15090114
APA StylePietrucha-Urbanik, K. (2026). Resource-Oriented Prioritisation of Water-Supply Pipe Groups Using Repair and Service-Interruption Burdens. Resources, 15(9), 114. https://doi.org/10.3390/resources15090114
