Computing a Model for Asset Management with Risk - Global Drinking Water Management and Conservation - page 185

Fig. 8.18 The service cost of
this asset is minimized if it is
renewed approximately every
25 - 35 years. However, this
value appears to be negative

Fig. 8.19 Iterative
adjustment reveals that the
precise solution is 30.2 years

Since the cost function resembles a sine wave, the function y ¼ sin ðÞ was

adjusted to fit the nonparametric regression. First, a value of 5,100 was added to the

right side of the equation so that the function would oscillate above and below the
mean. Next, we multiply the sine term by 300 to ensure that these oscillations occur
between 4,800 and 5,400. Lastly, the term inside the brackets was changed to
4 x 1

5 to ensure that the cycle time was 8 years and to ensure that the minima and
maxima coincided with the nonparametric regression. These manipulations resulted
in Eq. 8.22 for cost:

: