Introduction to Water Infrastructure Asset Management - Global Drinking Water Management and Conservation - page 166

7.4.3.3 What Are S and F?

In a nutshell, S and F are the modular components of risk. They can represent any
type of risk that the utility is concerned with. The utility is limited only by the
information it possesses. If data exist on the frequency and costs of a variety of
accidents then these events can be statistically modeled and included in the DSS to
determine the optimal renewal time in light of these risks. The utility can also
simulate risk reductions and the impact that this may have on the renewal interval
and on costs over the in nite horizon.

These have been referred to as modular components since they can be handled
separately from the rest of the model. A number of different risks can be
enumerated and included into this module that can, in turn, be used into the DSS.
The utility will be faced with n different risks, each with its own risk cost in period
i. The risk weighted cost of risk j in a given time period is:

S j F j

The aggregate risk weighted cost in a given time period is:

SF ¼ X

n

S j F j

j¼1

where, in discrete time:

¼ S i

S j

¼ F i F j

SF ¼ S i F i

and, in continuous time:

S j ¼ S j

ðÞ

F j ¼ F j ðÞ

SF ¼ S ðÞ F ðÞ

cation of SF, this module can be
included into the DSS to derive the optimal renewal interval.

Using statistical information in the speci