Civil Engineering Reference
In-Depth Information
3. The probability that the project will finish before day 30
4. The probability that the project will finish on day 32
5. The probability that the project will finish no later than day 35
6. The probability that the project will finish at least 2 days early
7. The probability that the project will finish at least 2 days late
8. The probability that the project will finish on day 32
±
1day
9. The completion date with at least a 90% confidence level
Solution
Before computing any of the nine values, we need to calculate the expected
duration
(
T
E
)
and the standard deviation
(σ
E
)
of the path ABCDE. We start
by performing the calculations for the individual activities. For every activity,
we calculate the expected duration
(
T
e
)
and standard deviation
(σ
e
)
by using
equations 11.1 and 11.2. After this, we calculate the variance
(
V
e
)
by using
equation 11.3. We tabulate the results as shown next.
Duration
Activity Optimistic
(
To
)
Most
Likely (
Tm
)
Pessimistic
(
Tp
)
Expected
Duration (
Te
)
Standard
Deviation (
σ
e
)
Variance
V
e
=σ
e
A
2
4
7
4
.
167
0
.
833
0
.
694
B
5
8
14
8
.
500
1
.
500
2
.
250
C
4
6
8
6
.
000
0
.
667
0
.
444
D
2
2
2
2
.
000
0
0
E
7
10
21
11
.
333
2
.
333
5
.
444
TE
=
32
VE
=
8.833
The next step is to do the calculations for the entire path. We simply add
the expected durations and variances, as explained in equations 11.4 and
11.5, to obtain
T
E
and
V
E
.
Next, take the square root of
V
E
(use equation 11.6) to find the standard
deviation
(σ
E
)
of the path:
T
E
=
32 days
V
E
=
8
.
833 days
and
σ
E
=
√
8
.
833
=
2
.
972 days
n
∑
Note that
σ
E
≠
(σ
E
)
i
i
=
1
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