What is the difference between MTBF and MTBCF?

Usually, mean time between critical failure (MTBCF) is a term used when redundancy exists in a system. It is often used to differentiate system reliability from series mean time between failure (MTBF).  Series MTBF, or simply MTBF typically includes all failures without regard to any fault tolerance that may exist, whereas, the “C” in MTBCF indicates that only “critical” failures are counted, i.e., those that will cause the system to not meet specification requirements. That said, MTBF is sometimes used to really mean MTBCF.  This is often  organization and/or industry dependent – if unsure, ask!