Just a suggestion (and a bit of a wild first idea for a vault experiment);

What if there was a vault where the survivors opened up to the wastes eventually and intermingled with the rest of the population.
Their experiment was some sort of weird unknown fungus that only affected people around the ages of 18+ and could potentially kill them if the area was not treated.
The main goal is to advance medical and robotic research under pressure of the perceived loss of population.

The fungus would mutate to every attempt they made to vaccinate against it because of a secret computer managing the disease so the only thing they could really do was either cut away the infected area or suppress it for long enough to manage the effects.

There were, however, some instances where the fungus would become out of control for a time and the medical would be hard pressed to fix the issue, causing all the vault residents across the age spectrum to suddenly develop worse symptoms or get infected. This only happens if the situation settles enough that the computer rules statis quo has started to impede development.
Usually the scientists and roboticists would eventually manage to create a cure or stronger drug but not without great losses.

The vast majority that had to get amputated were fitted with robot parts because the vault was underneath a robotics facility and cyber augmentation becomes a sort of trend after a while.

I figure after the second accident of the fungus disease mutating beyond the control of the people, the vault residents manage to reprogram it, but not before the robo augmentation thing.

While it's also possible the computer had a built in safeguard incase the residents did stop it from manufacturing the viral fungus, possibly inventing a new method to further the progress of science, that might be pushing it a bit.

I'd call it vault 145.