The variable A
is typically called the Availability
. Reliability is the probability of working at a particular time under specific circumstances. Availability typically considered a constant (a long-term average of how much of the time the system is available); reliability decreases with time.
The two are obviously related, but not the same. A common function to express reliability is
R = exp(-t/MTTF)
but the actual function to use depends on the situation.
MTBF = A x MTTR/(1-A)
What's this ? MTBF is directly proportional to MTTR, which means the longer my MTTR, the better my MTBF !!! This is contrary to the original basic concept, that a short MTTR is best.
Ah, but MTBF is not
directly proportional to MTTR. MTBF also
depends on A
, which in turn depends on MTTR. So when you change, MTTR, you also change A
With a little algebra, it is easy to show that the equation above reduces to
MTBF = MTFB
In other words, MTBF in independent of MTTR, as would be expected.
If you did want to use this equation to calculate to MTBF, you would need the MTTR of the system
. This would be some sort of average of the MTTR for each element combined with the probability of each component actually failing.
To calculate the MTBF, the best answer is probably just to go back to the original numbers. If you know the MTBF for each element and the appropriate series & parallel combinations, you should be able to find the overall MTBF directly.