Environmental Engineering Reference
In-Depth Information
0.2917 x 0.0012 = 0.583. Finally, the overall reliability factor of the whole system, from
Equation 2.11, is 0.833.
Table 2.7
Sample of the reliability calculation based on the method of Cullinane
Node
Pipe
RE
ij
1
2
3
4
5
6
7
8
average
R
1i
R
1
RE
1i
R
2i
R
2
RE
2i
R
3i
R
3
RE
3i
R
4i
R
4
RE
4i
R
5i
R
5
RE
5i
R
6i
R
6
RE
6i
1
0
0.9988
0.5417
0
0.5410
0.8750
0
0.8740
0.5833
0
0.5827
1
0
0.9988
1
0
0.9988
1
1
1
0.5417
0
0.5410
0.8750
0
0.8740
0.5833
0
0.5827
1
0
0.9988
1
0
0.9988
1
1
1
0.5417
0.5417
0.5417
0.8750
0.4167
0.8745
0.5833
0.2917
0.5830
1
0.8750
0.9999
1
0.8750
0.9999
1
1
1
0.5417
0.5417
0.5417
0.8750
0.8750
0.8750
0.8533
0.5417
0.5832
1
0.9167
0.9998
1
0.9167
0.9998
1
1
1
0.5417
0.5417
0.5417
0.8750
0.8750
0.8750
0.5833
0.5833
0.5833
1
1
1
1
1
1
1
1
1
0.5417
0.5417
0.5417
0.8750
0.8750
0.8750
0.5833
0.6250
0.5834
1
1
1
1
0.8333
0.9997
1
1
1
0.5417
0.5417
0.5417
0.8750
0.8333
0.8749
0.5833
0.5833
0.5833
1
0.9167
0.9998
1
0.6667
0.9992
1
1
1
0.5417
0.5417
0.5417
0.8750
0.8750
0.8750
0.5833
0.5833
0.5833
1
0.8333
0.9996
1
0.8333
0.9996
0.9999
n1
0.5415
n2
0.8747
n3
0.5831
n4
0.9996
n5
0.9995
n6
2.5.2 Reliability Based on Demand Reduction Analysis
The second group of the methods that look into the network reliability by analysing single
pipe failures are those based on the assessment of the demand reduction inflicted by the
failure. The overall network reliability factor can be determined by a simplified formula:
Q
−
Q
f
R
= 1
−
2.12
Q
where
Q
f
represents the available demand in the system after the pipe failure, against the
original demand
Q
. The approach suggested by Ozger and Mays (2003) takes into
consideration the probabilities of the pipe failures; the system reliability is expressed in terms
of
available demand fraction
(ADF) under the minimum required service pressure:
1
m
∑
=
j
net
R
=
1
−
(
−
ADF
)
P
2.13
j
m
j
1
where
ADF
net
is the network available demand fraction resulting from the failure of pipe
j
,
P
j
is the probability of the failure of that pipe, and
m
is the total number of pipes in the network.
In the above equation,
P
j
is determined by using the Poission probability distribution
described by Equation 2.6. In calculation of the system availability, this method considers the
first and the second order failures:
Search WWH ::
Custom Search