When building an important computer system triple redundance is built in. ie three processors normal working together but one can do the job of three if the others break down.
Quick rough answers:
If you are specifically referring to redudancy, then in the simplest system all three processors will perform the same job and then voting circuitry will ensure that the "correct" result is given in the case one processor fails.
You can get redundancy in other ways, eg: providing over capacity as might be done in certain "cloud" scenarios etc. Anyway, there are many, many forms of system redundancy. I think in your example however you're referring to a parallel processing system in which load can be shared - that's different case to fault-tolerance which is really the case for railways.
There are a number of issues in such systems, this article gives a good overview of the most famous of these:
https://en.wikipedia.org/wiki/Byzantine_fault_tolerance
Then someone mentioned avionics and fail-safe. In a simple system, eg: a signal, then if something fails then the system fails to a safer state, eg: if a yellow bulb fails in a 4-aspect signal then either no signal is shown or only a single yellow is shown, both of which are more restrictive then a double yellow.
You can get variations of this, eg: circuitry which ensures that a red is shown for any failure.
The main point here is to get a system to fail *gracefully*. For example, in Airbus the general principle is that the system under failure returns more and more control, gracefully, to the pilot, eventually leaving the pilot with full control. And yes, Airbus aircraft can be flown fully manually.
One interesting point to note is that in such systems pretty much everything is done to avoid the system giving up and handing all control over to a human at once.
Big topic to discuss, if you have anything specific let me know by PM or reply here,
t.
Ian