If you optimize for MTBF, you optimize for it to be a long time between failures. You optimize for the system not going down in the first place, but when it does do down it might be Pretty Bad.
If you optimize for MTTR, you don't care how often you go down and instead optimize your recovery time to be as short as possible.
If you optimize for MTTR, you don't care how often you go down and instead optimize your recovery time to be as short as possible.
The concepts are pre-computing.