The classic way of calculating the length of the project buffer for a critical chain is to throw away half the assumed saftey quoted in each task and then put the remaining half at the end of the chain as the project buffer. Has anyone done any research into how much safety really is included in the quoted time for each task in particular industries? Anyway, how do we know that half the length of the trimmed critical chain is appropriate as a project buffer?
The mathematics of combining the skewed probablity distributions of each task in the critical chain are not that simple. The resulting distribution curve for the entire critical chain has an extremely long tail and a very low "body". If we look at the median of this curve then it is way to the right of the sum of the medians of the individual critical chain tasks. So just adding up the (trimmed) estimated task times does not give us anywhere near the correct answer for the duration of the project which gives us a 50-50 chance of finishing it on time, ie the project buffer should start much later than we are told. The fact that projects run using critical chain project management finish on time therefore implies that there is still too much safety in those projects.
On the other hand, if we look at the duration which gives us a 90% probability of finishing the project on time then we find it is way to the left of the the sum of the 90% times for each task. So the overall project is relatively much less risky than any individual task.

The result is that the level of safely required for the entire critical chain (ie the project buffer) is much less (proportionately) than is required for any individual project, which justifies Goldratt's claim that we can throw away much of the assumed saftey in each task. How long should the project buffer be? Unless we know the real distribution curves for the tasks involved then we cannot know and this is why we need evidence from particular industries in order to build some heuristics.





