Environmental Engineering Reference
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via regression analysis. The discount rate was the 10-year bond yield and is given as
4.23 percent. 3 These networks are pipe networks, for which there is no maintenance
expense. An approximate investment cost is determined for each city by taking half
the value of all failure costs over the sample period. This is only an approximation
for purpose of demonstration and compensates for data de
ciencies. Lastly, when
variables are found not to be statistically signi
cant, they take on the mean value
during solution of the model. This is because the model gives the optimal renewal
of the network as a whole.
8.4.2 City A
The replacement cost of the network of City A will be set at half of the sum total of
all the expenses arising from failure from 1986 to 2005. This amount is $41,278.
8.4.2.1 Determination of S(x)
In order to determine S(x), the cost of failure was regressed on all the variables
collected from the regional municipality. After correcting for multicollinearity,
heteroscedasticity and non-normality, the signi
ed and
the following Eq. 8.1 was estimated for the cost of failure to be used in the solution:
cant variables were identi
S ðÞ¼ 6362 þ 673
38
7 : 05
:
Depth i þ 126
19
3 : 278
:
Age i
ð 8 : 8 Þ
ð
Þ
ð
Þ
8.4.2.2 Determination of F(x)
The function representing the frequency of failure for City A network was deter-
mined by regressing frequency of failure on age. It turned out that non-normality
was again an issue. To resolve non-normality, a Robust LAE regression was per-
formed. The following Eq. 8.2 for age was estimated:
F ðÞ¼ 7
:
5947 þ 0
:
ð 8 : 9 Þ
25789
0
Age i
ð
:
0788
Þ
8.4.2.3 Solution of the DSS
In the above regression analysis, the two most important parameters of the DSS
were determined: Eqs. 8.8 and 8.9 . These two modular parameters can now be
added to the DSS in order to determine the optimal renewal period for the water
network in City A. The cost-minimizing model from Sect. 7.2.3 is Eq. 7.8 :
3
This was the 10-year bond yield in 2007; but this can be easily varied.
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