Project Controls: Producing a Horizontal Split P50 curve

From a deterministic schedule you cannot determine float distribution probabilities. You must use some modeling to iterate hundreds or thousand times your schedule with varying duration and risk distributions. Then the software will record for each activity the resulting dates as well as float values for each iteration and from this data it will generate the cumulative distribution curves.

Originally when PERT was in its infancy the developers thought that the cumulative probability curve could be obtained from a fixed critical path, the deterministic schedule critical path. They soon found it was leaving out some occurrences of other critical paths and corrected the math using Monte Carlo Simulation to generate the risk events and run the iteration, then again using Monte Carlo  would generate the risk events and run again the schedule iteration.

http://hkarms.myftp.org/web_resources/Conference_Presentation/CPM_PERT_Schde_RIsk_Anlys_Consttn.pdf

Note that in the prior reference the probabilities of success from a traditional PERT computation differ from the Monte Carlo simulation. Perhaps those who adopted names similar to PERT in their risk software did not realized that PERT was at some point in time associated with a wrong assumption, that near critical path do not matter. That float is always free; but it comes at some cost in your probabilities of success.

I never liked the name PERT because it tends to forget a lesson no one doing risk analysis shall forget. The new name Oracle is adopting without reference to PERT I welcome.

From: http://en.wikipedia.org/wiki/Monte_Carlo_method

Monte Carlo methods vary, but tend to follow a particular pattern:

1. Define a domain of possible inputs.
2. Generate inputs randomly from a probability distribution over the domain.
3. Perform a deterministic computation on the inputs.
4. Aggregate the results.

The interrelationships on a CPM schedule are so complicated that is only through simulation these curves can be correctly generated.

Usually the float cummulative distribution curve is an output, not an input in traditional schedule risk software.