How can PERT help us at project level?

If we assume that all five the activities are o n the critical path and that they will all be done sequentially, then it is estimated that it will take 60.3 days to complete the project. But we also saw from the PERT calculations on activity level that there is uncertainty regarding the estimates for every activity. Therefore there is a probability that any activity can take longer or shorter than the PERT estimate to be completed. Because we do not know which activities will take shorter and which will take longer the only option is to accept that some will take less time and some will take more time to be completed. This means that it will be unrealistic to ad up all the sigma values and make them applicable to the critical path. However, there is a more realistic way to calculate the uncertainty of how long it will take to complete the entire project. We can calculate a more realistic standard deviation for the critical path by using the formula "Project critical path Sigma = √(sum of all PERT variances)". We need to determine the PERT variances for this formula by calculating sigma square (sigma X sigma). Then we add all the PERT variances together and calculate the square root of the sum. This calculation gives a more realistic standard deviation that can be used to express the uncertainty applicable to the project due date. The following table shows the individual values of the PERT variance for every PERT standard deviation:

The project standard deviation can be calculated by determining the square root of the sum of the PERT variances. As per the above table the sum of the PERT variances is 41.8. The square root of 41.8 is 6.5. Therefore one standard deviation for the project as a whole is 6.5 days. This value can now be used to calculate the values for one, two and three sigma for the total project:

• There is a 68% probability that the project will be completed between 53.8 and 66.8 days.

• There is a 95% probability that the project will be completed between 47.3 and 73.3 days.

• There is a 99.7% probability that the project will be completed between 40.8 and 79.8 days.

In practice these percentages can be used to indicate to the sponsor that, due to the uncertainty regarding the estimates, there is a:

• 50% probability that the project will be completed within 60 days.

• 68% probability that the project will be completed within 67 days.

• 95% probability that the project will be completed within 73 days.

• 99.7% probability that the project will be completed within 80 days.