# Statistics Calculation for Activity Time

From the beta distribution, the expected or average time for each activity is calculated according to the following equation:

T _ T0 + 4 Tm + Tp

where T = average time, To = optimistic, Tp = pessimistic time, and Tm = most likely time.

4.5.72 Example

For the previous example of constructing the concrete foundation, there are three values for time for each activity, as shown in the following table.

Table 4.4 PERT example

 Item Activity To Tm Tp 1 Mobilization 1 3 5 2 Excavation 6 8 11 3 (Pouring concrete foundation and piping support) 8 16 25 4 Install the piping 3 4 5 5 Install the mechanical package 1 1 2 6 Put the grouting 1 1 3 7 Connect the piping 2 5 7 8 Commissioning and start up 1 1 2

After defining the critical path from the previous example, calcu­late the expected time at each activity as shown in Equation (4.1). Calculate the standard deviation using the following equation:

T – T

1 P l0

6

Variance, V, = S2.

From Table (4.5) calculate the Та, which is the average time and the standard deviation based on Equations (4.1) and (4.2), respectively. The variance is calculated as it is only possible to sum the variance. You cannot perform summation for the standard deviation.

The minimum time to finish the project is 18 days, and the maxi­mum time to finish is 39 days. The average time period to finish the project is in 23.31 days.

What is the probability if you increase the project time over 25 days? This value can be calculated from the following equation:

V = 0.44 + 0.694 +1.36 + 0.028 + 0.11 + 0.11 = 2.74 days.

 Item Activity V S C. P. Та To Tm Tp 100 Mobilization 0.44 0.67 * 3 1 3 5 200 Excavation 0.694 0.83 * 8.3 6 8 11 300 (Pouring concrete foundation and piping support) 1.36 0.5 * 7.17 8 10 15 400 Install the piping 0.11 0.33 4 3 4 5 500 Install the mechanical package 0.028 0.167 * 1.17 1 1 2 600 Put the grouting 0.11 0.333 * 2.17 1 1 3 700 Connect the piping 0.694 0.833 3 2 5 7 800 Commissioning and start up 0.111 0.333 * 1.5 1 2 3
 Table 4.5 PERT calculation

Standard deviation (S) = 1.66 day.

From the probability distribution tables, the probability that the project completion period is more than 26 days is 5%. The prob­ability that the execution time for the project is equal to or less than 26 days is 95%, as shown in Figure (4.13).