MTBF (Mean Time Between Failure) of a system is the time between two successive failures of the system. It is the sum of the MDT (Mean Down Time) and MTTF (Mean Time to Failure). Assume that the MTBF of the system is six months and that there are on average two failures in a year. The frequency of failure of the system is two per year. There exists a reciprocal relationship between MTBF and failure frequency (which is discussed on page 8-23.) Therefore, if v is the steady-state failure frequency of the system, then:

For the example problem:

Therefore:

If λ<<μ, then MTBF=1/λ. This relationship is commonly employed elsewhere in this document.

Once MTBF has been obtained, MTTF and MTTR can easily be found:

All of the methods provided in this section are exact methods. Approximate solutions are useful for solving large practical problems within a short time.