Introduction to Water Infrastructure Asset Management - Global Drinking Water Management and Conservation - page 155

Shipping costs may also increase. Type 2 and 3 failures may result in illnesses
leading to a greater number of sick days.
Temporary replacement costs refer to those costs that become necessary, as an
alternative source of water needs to be mobilized. At times this cost may refer to an
alternative for water as opposed to an alternative source. Typically, this will result
from a Type 3 failure. However, this cost may be necessary under Type 1 and 2
failures as well. Communication costs refer to any costs originating from the need
to communicate road closures, boil water advisories, etc. Health costs refer to all
health costs resulting from illnesses caused by any of the failure types. These
illnesses range from the very serious (say bacterial infection caused by E. Coli)to
the very minor (slight dehydration). It is important that all costs are recorded only
once. For example, health costs include all forms of medical treatment, but do not
include lost wages, as lost wages are an economic cost. Hence, there should be no
duplication of costs.

7.2.2.3 Risk Measurement

The primary measurement of risk is expected risk. This is simply the probability of
a failure occurring multiplied by cost of that failure:

P i C i

where,
P i is the probability that failure i occurs, and

C i is the cost of failure i, should it occur

In the event that there are n possible failures that may occur, the expected cost of
failure is the sum of all the probabilities of failure multiplied by their respective
costs:

X

n

P i C ii

i¼1

where, P i and C i are as above, and n is the number of different failures.
In the event that a failure may experience varying degrees of severity, the
expected cost of failure is the integral, from the lowest severity to the highest
severity, of the probability of failure multiplied by the cost of the failure:

Z S

P ð x Þ C ð x Þ dx

S