Project Management in the Oil and Gas Industry

Equation:
 
f x
T
x
e
x
1
1
/
 
(2.27)
Mean:
 
x
 
(2.28)
0
0.00
0.05
0.10
Densit
y
0.15
5
10
X
Poisson distribution, lambda = 5
15
Figure 2.11 The exponential distribution.

---

Project Economic Analysis 65
Standard Equation:
 
s
2
 
(2.29)
The different shapes of gamma distribution are presented in Figure 2.14.
2.3.2.8 Logistic 
Distribution
This distribution is used frequently to describe the population growth rate in 
a given period of time. It can also represent interactions between chemicals.
f x
s
e
s
e
x
s
x
s
; ,
1
2
(2.30)
1
0.75
0.5
0.25
0
0
1
X
F(x)
2
3
4
5
Figure 2.12 The exponential distribution.
0
0.5
0.1
1.5
x / 
2.0
2.5
3.0
=1.5
=3.2
=5
=0.5
=1
P
robability densit
y
Figure 2.13 Weibull Distribution.

---

66 Project Management in the Oil and Gas Industry
2.3.2.9 Extreme Value (Gumbel Distribution)
This distribution is used when the intended expression of the maximum 
value of the event occurs in a period of time. Therefore, it is used for floods, 
earthquakes, or rain and is used to calculate the loads on the plane and 
study the fracture resistance of some materials.
 
f z
z u
e
z
z u
( )
exp
(
)
(
)
(2.31)
F z
e
z
z u
( )
exp(
)
(
)
1
,
(2.32)
where –∞ ≤ z ≤ ∞.
 
m
u
z
.
 
(2.33)
 
z
6
.
(2.34)
2.3.2.10 Pareto 
Distribution
This distribution is commonly used when characterizing per capita income, 
a change in stock price, the size of the population in a city, the number of 
staff in a company, as well as the errors that occur in a communications 
circuits. It also represents changes in natural resources.
0.5
k = 1, = 2.0
k = 2, = 2.0
k = 3, = 2.0
k = 5, = 1.0
k = 9, = 0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
8
10
12
14
16
18
20
Figure 2.14 Gamma distribution.

---

Project Economic Analysis 67
It uses the Pareto principal, which is based on the idea that by doing 
twenty percent of the work, 80 percent of the advantage of doing the entire 
job can be generated. Or, in terms of quality improvement, a large major-
ity of problems (80 percent) is produced by a few key causes (20 percent).
2.3.3 Distribution for Uncertainty Parameters
There are some variables that are difficult to identify in distributions, such 
as the project estimate cost or the experiments and tests necessary to study 
the phenomenon that are very expensive, such as defining the area and 
height of an oil reservoir, so we use the following distributions.
2.3.3.1 Triangular 
Distribution
This distribution is very important in the case of phenomenon where 
testing is very expensive. An example is when you select the size of an 
underground reservoir and three tests are usually performed to obtain 
the minimum, the maximum, and most likely. This distribution is used in 
schedule planning, which will be discussed in Chapter 4, and it determines 
the time required to complete the activity by three values, a minimum 
time, maximum time, and the most likely time to finish that activity.
In addition, it is also used to determine the estimated cost of a proj-
ect where the maximum allowable value is about a ten to fifteen percent 
increase on the cost and the calculated minimum value is a ten to fifteen 
percent decrease for the calculated cost.
0.3
0.2
0.1
0
–5
0
5
10
= 5 s = 2
= 9 s = 3
= 9 s = 4
= 6 s = 2
= 2 s = 1
15
20
Figure 2.15 Logistic distribution.

---

68 Project Management in the Oil and Gas Industry
Triangular distribution is shown in Figure 2.17 where x
1
, x
2
, and x
m
are 
the minimum, maximum, and most likely values, respectively.