# 6.3.2 Pert technique contd.

Here are the steps involved in determining the probabilities associated with various completion times. We will illustrate using the previous example

1. Calculate the total variance for the activities on the critical path.  From the previous the unit the critical path tasks were A, C, E, G. The variance of these tasks added together  is σ2cp= 1.78+.11+.44+.44=2.77
2. Assuming the completion times follow a normal distribution , calculate the Z value for a given D as follows Z = (D-µ)/√σ2cp,                    Where D is the duration and µ is the mean completion time.

Using our example, Z= (25-23)/√2.77 = 1.20

3. Using the normal distribution table read the corresponding probability ( area under the curve) for a Z value of 1.20. The answer is 88.5%. That is we have an 88.5% probability of completing the project in 25 weeks or less.  There should be a normal distribution table at the back of your textbook.  Here is a table that you can use cumulative-normal-distribution-tablex

4. To find the probability for 20 weeks, repeat the above steps. Your Z value will be negative. Read the probability for the positive Z value and subtract from 100 to get the answer.  The answer is 3.6%.

Here is an example to practice to make sure you understand these concept.  PERT-Practice-Problem The answer is shown on the next page.

Before we leave this topic, it is important to note that the accuracy of your schedules also depends on the correct identification of all precedence relationships. Take a look at this comic strip precedence