Schedule Risk Management - Construction Project Scheduling and Control - page 387

EXPECTED VALUE
Statisticians combine the likelihoods of different outcomes of an event with their cor-
responding potential consequences in what is known as the expected value :
E ( X )= ∑
i

x i p ( x i )

⋅

where

E ( X ) = the “expected value” of an event, X, such as an accident, hurricane, or
shop drawing rejection
i = the domain of all possible outcomes, such as catastrophic, severe,
significant, mild, light, negligible
p ( x i ) = the probability of occurrence of outcome i
x i = the value of consequence of outcome i

For example, for a hurricane that may strike the area where a project is located,
the following likelihoods and outcomes are estimated:

Outcome Likelihood Impact on Schedule

Negligible 20% No delay

Mild 30% 5-day delay

Significant 25% 12-day delay

Major 20% 20-day delay

Catastrophic 5% 50-day delay

The expected value of the hurricane event is

E = 0 . 20 0 + 0 . 30 5 + 0 . 25 12 + 0 . 20 20 + 0 . 05 50 = 11days

⋅ ⋅ ⋅ ⋅ ⋅

It is important to note that the expected value is a hypothetical, not real, value. It
is adjusted by the likelihood of its occurrence. However, the party assuming the risk
must account for the possibility of all outcomes and whether or not he can take that
risk. In the preceding example, there is a likelihood, albeit small, that a catastrophic
hurricane will cause a 50-day delay in the completion of the project. The contractor
and owner must bear in mind that such an outcome may happen.
In a different example, a 55-year-old woman is contemplating investing her entire
savings in an investment venture with several possible outcomes:

Outcome Likelihood

Double her money 20%

Make a 50% profit 30%

Break even 30%

Lose her money 20%