Shewhart control charts with a centerline, three WLs, and a single CL were constructed from the historical data set generated (Figure 3) for each potential meter location (i.e., all nodes and pipes). The mean nodal pressures and pipe flow rates vary over time because of the diurnal demand pattern. While the variances of pipe flow rates are relatively constant through the day, the nodal pressures have high uncertainty during peak demand hours, resulting in wider CLs. Low variations in nodal pressure were observed at night and early morning because of the low demand and low variability during these periods. Control and out-of-control measurements were evaluated as per the WEC rules, using the Shewhart control chart for the desired meter location, to construct the false alarm and detection matrices, respectively. The results for a pressure meter installed at node 15 and representing 15 burst events are summarized in Table 1.
Detection information using pressure meter at node 15
Burst events . | Detection (Yes/No) . | Detected by rule . | ||||||
---|---|---|---|---|---|---|---|---|
Event ID . | Location (node ID) . | Burst time index* . | Detection time index . | Time to detect (h) . | Emitter coefficient . | Burst flow rate (lps) . | ||
1 | 89 | 307 | 314 | 0.6 | 29 | 16.6 | Yes | 4 |
2 | 77 | 345 | 8 | 4.0 | No | |||
3 | 26 | 522 | 13 | 6.5 | No | |||
4 | 22 | 504 | 910 | 33.8 | 15 | 7.5 | Yes | 1 |
5 | 35 | 56 | 57 | 0.1 | 41 | 22.2 | Yes | 1 |
6 | 76 | 291 | 313 | 1.8 | 27 | 14.4 | Yes | 1 |
7 | 108 | 378 | 540 | 13.5 | 32 | 18.3 | Yes | 1 |
8 | 99 | 444 | 848 | 33.7 | 9 | 5.2 | Yes | 1 |
9 | 48 | 92 | 13 | 7.3 | No | |||
10 | 59 | 92 | 281 | 15.8 | 29 | 15.5 | Yes | 4 |
11 | 94 | 516 | 563 | 3.9 | 48 | 27.4 | Yes | 2 |
12 | 5 | 320 | 330 | 0.8 | 45 | 20.1 | Yes | 1 |
13 | 5 | 58 | 586 | 44.0 | 23 | 10.3 | Yes | 3 |
14 | 34 | 316 | 320 | 0.3 | 38 | 20.5 | Yes | 2 |
15 | 61 | 406 | 10 | 5.3 | No |
Burst events . | Detection (Yes/No) . | Detected by rule . | ||||||
---|---|---|---|---|---|---|---|---|
Event ID . | Location (node ID) . | Burst time index* . | Detection time index . | Time to detect (h) . | Emitter coefficient . | Burst flow rate (lps) . | ||
1 | 89 | 307 | 314 | 0.6 | 29 | 16.6 | Yes | 4 |
2 | 77 | 345 | 8 | 4.0 | No | |||
3 | 26 | 522 | 13 | 6.5 | No | |||
4 | 22 | 504 | 910 | 33.8 | 15 | 7.5 | Yes | 1 |
5 | 35 | 56 | 57 | 0.1 | 41 | 22.2 | Yes | 1 |
6 | 76 | 291 | 313 | 1.8 | 27 | 14.4 | Yes | 1 |
7 | 108 | 378 | 540 | 13.5 | 32 | 18.3 | Yes | 1 |
8 | 99 | 444 | 848 | 33.7 | 9 | 5.2 | Yes | 1 |
9 | 48 | 92 | 13 | 7.3 | No | |||
10 | 59 | 92 | 281 | 15.8 | 29 | 15.5 | Yes | 4 |
11 | 94 | 516 | 563 | 3.9 | 48 | 27.4 | Yes | 2 |
12 | 5 | 320 | 330 | 0.8 | 45 | 20.1 | Yes | 1 |
13 | 5 | 58 | 586 | 44.0 | 23 | 10.3 | Yes | 3 |
14 | 34 | 316 | 320 | 0.3 | 38 | 20.5 | Yes | 2 |
15 | 61 | 406 | 10 | 5.3 | No |
*Burst time index refers to the index of time, starting from a value of 0 at midnight and increasing by 1 every 5 min.