[This started as a comment, but I ran out of room. So, I'm posting as an answer.]
If only one of the following can be improved due to whatever reason, what's more important: ensuring double the availability of the service or double the mean time between failures?
The relative importance of availability vs. MTBF depends on the usage of the system. I'm going to assume that user's work is lost when failures occur.
If the users work in short sessions (much shorter than MTBF), then work is rarely lost to failures. In this case, the uses might not even notice failures. In this case, availability may be a greater issue than MTBF.
If the users work in long sessions (comparable in length to MTBF), then work is more likely to be lost due to failures. Loss of work tends to be more annoying than unavailability of the system. In this case, MTBF may be a greater issue than availability.