Aside: I may be reading too much between the lines of this question; I think this is a workplace politics problem rather than a strict PM problem. As a consequence, my answer is correspondingly pessimistic, jaded and cynical.
What is the probability that the functional unit will fail to deliver? What is the impact on the project scope/schedule/quality?
There is usually no hard data on which to base these two estimates; that leaves you with two subjective estimates, which is an unpleasant place to be in an inter-office argument. I would develop some estimates based on assumptions.
- Assume that Functional Unit X will miss their JIT target 70% of the
time, by less than two business days; what happens to my schedule.
- Assume that Functional Unit X will miss their JIT target 10% of the
time by more than 5 business days.
- Assume that Functional Unit X will hit their target, but the product
will be unsatisfactory for our needs from a QC point of view. (speed
increases defects; catch those before they become your problem.)
Then develop risk mitigations.
- IF Functional Unit X missed their JIT delivery, then we could purchase
from competitor Y. It would cost 30% more, but would permit us to
meet our deadline with acceptable quality."
- IF Functional unit X is more than 1 day late on their deliverable, then
we inform customer that our deadline will slip by X days, or by Y
- In order to compensate for the chance that Functional Unit X may miss
a JIT delivery, we will keep stock of Y on hand. (somewhat tougher with software).
- In order to deal with the risk, we are including an SLA that
Functional Unit X produce a prototype by date Y
Those are "pretty" textbook answers. Reality tends to be much less cosmetic. For most of us, those are totally unrealistic answers. But they demonstrate that you're aware of the problem and you're doing your best to work around it. The onus transfers to those who are doing less to solve the problem.
The hard nose gritty goal here is to convince management and stakeholders that you did more planning and *better planning" than the "kick it down the road" approach. If things go south, the guy who can demonstrate the better pre-planning will avoid some of the blowback. Your best chance is to proactively solve the problem; but sometimes we're dealt situations where the ton of bricks is already falling and the best we can do is shout a warning and get out of the way.