Both tools lead to the same end: a critial path and critical activities with slack time equal to zero. The differences between these tools come from how they treat the activity time. PERT treats activity time as a random variable whereas CPM requires a single deterministic time value for each activity. Another difference is that PERT focuses exclusively on the time variable whereas CPM includes the analysis of the Time/Cost Trade-off.

PERT

We have a high degree of uncertainty in regard to the completion time of many activities. It makes sense in the real world that you do not really know how long a particular activity will take, specially talking about certain activities such as research and development. In this case, we can look at the project completion time in a probabilistic fashion and for each activity we can define:

1. Optimistic time estimate: an estimate of the minimum time an activity will require.
2. Most likely time estimate: an estimate of the normal time an activity will require.
3. Pessimistic time estimate: an estimate of the maximum time an activity will require.

These three estimates are considered to be related in the form of unimodal probability distribution: m. What we need in any case is a specific duration for each activity taking into consideration these three estimates. This can be possible calculating the expected or mean activity time for each activity as

With the expected time for each activity we can determine which is the critical path. Using three assumptions, we can conclude that project completion time or critical path completion time has a normal distribution. Using this, we can determine probabilities, using completion time as a normal random variable, mean and standard deviation.

P(Completion Time <= 15.5 months) = P ( z <= 15.5 - mean/ standard deviation) =