PERT analysis and Project Risk Management
Program Evaluation and Review Technique (PERT) gives us the answer to a very critical question — What is the probability of completing a project within a given deadline?
To start with PERT analysis we first must know — What is the expected completion time of a project ?. And to calculate this we rely on critical path method (CPM).
According to CPM, a project scope should be broken down into simpler task which is called as the work breakdown structure. Some tasks can be independent where as some task can be dependent on the completion of other tasks.
These simpler tasks can then be used to create a project network. Below is an example of a work breakdown structure and a project network based on that.
Once we reach this stage, then we have to start on estimating each individual task in project network, this is generally based on your past experiences of project of similar kind or if it is a totally new kind of project you may have to rely on secondary sources of information to estimate tasks.
Each task has to be given 3 types of estimates: Optimistic, pessimistic and most likely.
Optimistic estimates (a): These estimates comes from your similar projects which you finished in the shortest time period.
Pessimistic estimates (b): These estimates comes from your worst performances, which took more than usual time to finish a project of similar kind.
Most likely estimates (m): These estimates are the average time you generally take to finish projects of similar kind.
Calculating Mean and Variance
But still, we don’t have the actual estimates for each task, for that we will calculate the Mean for these estimates using the μ = (a + 4m + b) / 6.
We will also calculate the variance for each activity in the project network which will further help us to calculate the probability of completing the project within a given deadline. For calculating the variance we will use σ = (β — α) / 6.
Based on the above mean calculations, we can now assign weightage (number of days required for each task) to each node, and then determine the most critical path which was our first objective
Critical path is nothing, but the path with highest weightage between start and finish.
In the above example, the critical path we have is ABCGHJ.
From now on for the project PERT analysis we will be using these nodes only, since any delay in these task will result in a project completion delay, while any task which is not a part of the critical path can have some Activity slack (delay in completion).
Activity slack is the amount of time each activity can be delayed by without exceeding the deadline.
Now we will use normal distribution method to calculate the probability of the completion of project within a given deadline.
Lets say, we need to find out if the above project can be completed in 85 working days or not?
We simply use the normal distribution function (easily available in excel), which takes 4 parameters as shown below.
Probability of completion within deadline
For the critical path ABCGIJ we get the following values.
Mean = 77
Std. Deviation (sqrt of variance)= 6.25
So,
prob. of finishing project in 85 days will be = NORM.DIST(85,77,6.25,1)
which comes out to be, 90%
Where as,
prob. of finishing project in 90 days will be = NORM.DIST(90,77,6.25,1)
which comes out to be, 98%
This can really help us in getting the correct estimate for a project timelines and thus any risks related to delays in the delivery of the project can be identified at initial stages. Projects which have very critical deadlines or have a penalty involved incase of delays can be estimated in advance and a realistic time estimate can be given upfront to the clients.
