Binominal Distribution

This distribution is used in the following situations:

• determination of geological hazards;

• calculation of the performance of the machine for the cost and the cost of spare parts;

• determination of the appropriate number of pumps with the appropriate pipeline size with the required fluid capacity and the number of additional machines;

• determination of the number of generators according to the requirement of the project and to determine the number of additional generators in the case of an emergency or malfunction in any machine.

To understand the nature of this distribution let us use the following:

Equation:

(3.19)

Mean:

x = n. f

Standard Deviation:

Table 3.12 Alternative for example 3

2-5000

3-5000

3-4000

10,000

0.9025

0.9928

12,000

0.8574

5,000

0.0950

0.0071

8,000

0.1354

0

0.0025

0.0001

4,000

0.0071

0

0.0001

Total

1.000

1.000

1.000

Avg. Reliability

0.9500

0.9963

0.9685

Figure 3.10 Binominal distribution.

the normal distribution is called the Probability Density Function (PDF). These PDF distribution curves are used in cases where descriptions of the natural phenomena or materials properties that can take any values, for example, when you calculate the heights of

people in the building that you are in. You will find that the lowest number, for example, is 120.5 cm, and the highest number is 180.4 cm, and the heights of people can be any number between those numbers. But in the case of the last example, the number of drill­ing wells is between 1 and 25 wells. If we calculate the probabil­ity of success for 20 wells, we cannot say that there is a possibility of drilling 20.5, for example, because you cannot drill half a well. Therefore, in this case the probability distribution will be called the Probability Mass Function (PMF). This is very important when choosing the suitable distribution, which should match the natural phenomena for these variables. When defining the probability dis­tributions for steel strength, oil price, or population, one should use the probability density function (PDF).