Civil Engineering Reference
In-Depth Information
The pessimistic duration is the duration under the worst-case scenario. Both values
must be within the realistic, although perhaps unlikely, realm of expectations.
The mean-weighted value for these three durations is called the
expected dura-
tion
(
T
e
). It is calculated as follows:
T
o
+ 4
T
m
+
T
p
6
T
e
=
(11.1)
and
T
p
) may be
adjusted, but the denominator must equal the sum of all of the weights. The weights
in equation 11.1 represent a population of durations made up of 16.7% (one-sixth)
optimistic (
T
o
); 66
The weights assigned to these times (coefficients of
T
o
,
T
m
,
.
7% (four-sixths) most
likely (
T
m
); and 16.7% (one-sixth)
pessimistic (
T
p
).
Several symbols are used in other textbooks to represent the mean (arithmetic
average), such as μ and
X
.
The standard deviation for the expected duration (σ
e
) is
T
p
−
T
o
6
σ
e
=
(11.2)
and the variance (
V
e
)is
V
e
=σ
e
(11.3)
Now, add the expected duration for all activities on the studied path (
T
E
),
n
∑
T
E
=
(
T
e
)
i
(11.4)
i
=1
The variance (
V
E
) and standard deviation (σ
E
)
for the entire path
are calculated as
n
∑
(σ
e
)
i
V
E
=
(11.5)
i
=1
and
σ
E
=
√
V
E
(11.6)
With the information just calculated for the examined path, we can calculate the
probability that an event will occur on or by a certain date (
T
S
) by using the normal
distribution formulas:
Z
=
T
S
−
T
E
σ
E
(11.7)
where
Z
(called the
Z-function
) represents the number of standard deviations (σ
E
)
away from the mean (
T
E
).
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