Whilst I'm happy that probabilistic methods of estimation get air time, I feel these sorts of posts give the lay person unearned confidence that they are suddenly far safer then they are. In most cases I find people don't know what should be planned, how it should be defined, measured, tracked or assured - and when combined with a lack of appreciation for Risk and how it should equally be defined, measured, tracked and controlled this is the core problem not idea of estimating itself.
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Usually it's of little consequence and the stakes are low, but it's this general lack of skill in such a large population of people who are doing it poorly that gives estimation such a bad reputation in the first place. The idea of estimation is not incorrect, it's that people aren't taught how to do it properly in the first place and industry continues to propagate the myth that it's simpler than it is. Often because it's mandated by those who don't understand it themselves.
Having played in many types of industries I have a thesis that much of what we do in planning and estimating has had real benefit in some areas historically - where there are clear, repeatable, measurable observations, certain types of construction and fabrication - but not others due to their success being tied to the method alone without account for how the nature of what is being measured.
Monte Carlo has very real and valuable uses in critical path method scheduling, but, as with most things, only when used appropriately. Weather is something that fits well, because it is cyclic, we have a lot of data, we can, ahead of time, to some degree, have a likely view of where and when things like hurricanes/cyclones will occur in a given period.
In the Australian North-West Shelf where I used to plan O&G maintenance dive campaigns, knowing how long it takes to get to an area, a diver to get to depth, perform a task, return safely and leave the area is the easy part. "Everything going to plan"* we should be able to do these x number of inspections/interventions in y number of days. But weather is where you can come unstuck. Sea state matters, there is always some chance that you will have to interrupt or postpone on a day because of conditions. We know there are roughly x number of these days per cyclone season and roughly how long we might not be able to work for but pay full rates for crew, equipment etc.. An at risk period for weather goes on to the end of the schedule as contingency and is drawn down as needed, but in some scenarios where in the network of activities these multi-day events occur can have varying impacts. Inserting a three day stand-down early on could have a greater impact on the end date than a three day stand-down right near the end if at the earlier time you are doing things that must be done in a continuous sequence with - if interrupted - will need you to repeat again from the beginning. Luckily there are tools we can use to not just look at the net effects of activities in a schedule network having their own distribution curves, but also injecting events, again with their own probabilities, randomly throughout the network during the run.
This gives you a much greater insight than a 'P90' estimate on your critical path, it gives you the sensitivity of activities in your network.
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This all assumes, of course, that what you have modelled (planned) reflects reality to some degree. A bad schedule with bad bounds will give you a bad result regardless. It doesn't matter how many times you simulate it.
*it rarely does