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Table 2

Calculations of disconnection probability of network in a period of 1 month

Min. cut-sets contain k pipes EkpkMin. cut-set (Ek.pd)Pipes in the min. cut-set Ek.pd (Ek.pd.[pd.1]; … ; Ek.pd.[pd.k])P (Ek.pd)P (Ek)
E1 E1.1 5–6 0.035211 0.0622 
E1.2 8–9 0.007042 
E1.3 9–10 0.021127 
E2 E2.1 1–3; 3–4 0.000198 7.6849 × 10−4 
E2.2 6–7; 6–8 0.000198 
E2.3 6–7; 7–8 0.000297 
E2.4 6–8; 7–8 7.439 × 10−5 
E3 E3.1 1–2; 1–3; 1–5 2.0955 × 10−6 4.3219 × 10−5 
E3.2 1–2; 1–5; 3–4 8.3820 × 10−6 
E3.3 1–2; 2–4; 2–5 5.2387 × 10−6 
E3.4 1–3; 2–4; 4–5 1.8336 × 10−6 
E3.5 1–5; 2–5; 4–5 1.8336 × 10−6 
E3.6 2–4; 3–4; 4–5 7.3342 × 10−6 
E4 E4.1 1–2; 1–3; 2–5; 4–5 8.6082 × 10−8 7.8458 × 10−7 
E4.2 1–2; 1–5; 2–4; 4–5 7.7474 × 10−8 
E4.3 1–2; 2–5; 3–4; 4–5 3.4433 × 10−7 
E4.4 1–3; 1–5; 2–4; 2–5 5.5339 × 10−8 
E4.5 1–5; 2–4; 2–5; 3–4 2.2136 × 10−7 
E5 (empty) – –  
 …  
E13 (empty) – –  
 Sum:  0.0630 
Min. cut-sets contain k pipes EkpkMin. cut-set (Ek.pd)Pipes in the min. cut-set Ek.pd (Ek.pd.[pd.1]; … ; Ek.pd.[pd.k])P (Ek.pd)P (Ek)
E1 E1.1 5–6 0.035211 0.0622 
E1.2 8–9 0.007042 
E1.3 9–10 0.021127 
E2 E2.1 1–3; 3–4 0.000198 7.6849 × 10−4 
E2.2 6–7; 6–8 0.000198 
E2.3 6–7; 7–8 0.000297 
E2.4 6–8; 7–8 7.439 × 10−5 
E3 E3.1 1–2; 1–3; 1–5 2.0955 × 10−6 4.3219 × 10−5 
E3.2 1–2; 1–5; 3–4 8.3820 × 10−6 
E3.3 1–2; 2–4; 2–5 5.2387 × 10−6 
E3.4 1–3; 2–4; 4–5 1.8336 × 10−6 
E3.5 1–5; 2–5; 4–5 1.8336 × 10−6 
E3.6 2–4; 3–4; 4–5 7.3342 × 10−6 
E4 E4.1 1–2; 1–3; 2–5; 4–5 8.6082 × 10−8 7.8458 × 10−7 
E4.2 1–2; 1–5; 2–4; 4–5 7.7474 × 10−8 
E4.3 1–2; 2–5; 3–4; 4–5 3.4433 × 10−7 
E4.4 1–3; 1–5; 2–4; 2–5 5.5339 × 10−8 
E4.5 1–5; 2–4; 2–5; 3–4 2.2136 × 10−7 
E5 (empty) – –  
 …  
E13 (empty) – –  
 Sum:  0.0630 
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