What types of errors would cause one of the tests to fail? Is it mostly testing for hardware errors, or are there any software logic errors that could make it to production, but be caught by one of the tests several months down the road? The only software related items I can think of are edge cases where a built in test is based on real time input. Kind of like running the calculations through multiple independent implementations of the software.
There's actually a decent probability of memory corruption in space applications due to radiation. So in addition to checking communication across busses, application checksums are typically run continuously.
Another thing that's software-related is if you've got a (rare) race condition. For example a data structure that gets corrupted if you have a particular series of nested interrupts.
Now, hopefully your system is set up such that race conditions cannot happen, but good luck with that.
