Project Management in the Oil and Gas Industry

Probability
x
1
x
2
Figure 2.18 Rectangular Distribution.

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70 Project Management in the Oil and Gas Industry
distributions. The most common methods used to choose the best prob-
ability distributions that match with the phenomena test results are the K-S 
and Chi square methods.
As mentioned earlier, there is a way to choose the appropriate distribu-
tion mathematically, but each distribution has certain properties.
If there is raw data, as in the example of concrete strength, do the same 
procedure to define the frequency tables and curve by trying to choose the 
best probability distribution that can match with this curve.
2.3.4.1 Chai Square Method
This method calculates the potential value obtained from the practical test 
(O) and we calculate the corresponding value when calculated from the 
mathematical equation for the probability distribution (E). We then apply 
the following equation where ( ) is what we repeat in calculating its value 
according to the number of groups identified previously, as in the previous 
example, ten times, so k equals 10 in the following equation:
2
2
1
O
E
E
i
i
i
i
k
(2.39).
We then apply it to other probability distributions and the distribution 
that gives less (
2
) will be the appropriate probability distribution to pres-
ent this phenomena or parameter.
Note from the previous equation that when we match distribution 
resulting from the practical test, the probability distribution be
2
= 0.
2.3.4.2 Kolmograv-Smirnov 
(K-S)
This method is considered to be the second most common method to test 
how close the distribution is to the probability distribution. 
For this method, the distribution is calculated by the assembly output of 
the test, in cumulative descending order and is in the same table of the pre-
vious concrete strength example. The cumulative value is calculated when 
using the suggested probability distribution and, from the following equa-
tion, we can calculate the difference between each of the two values from 
the suggested probability distribution and from the cumulative test data, 
according to the number of classes. The biggest difference is calculated in 
both the number of classes and is often the value of K and S which are 
selected as the best suitable probability distribution. 

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Project Economic Analysis 71
K
S
i
n
F X
i
n
X
i
max
(
)
( )
1
(2.40)