Managing
technical uncertainties
Statistics,
RAMS
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MTBF,
MTTF & Availability
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The MTBF (mean time between failure)
is the average time between two failures.
In practice the term MTBF is
used only for the constant failure rate case (b = Weibull shape = 1),
but mathematically this limitation is not
necessary. The constant
failure rate case is also called steady
state.
In the (more general) non steady
state case, the average time between two failures is a function of
time. We could still call this function MTBF(t), but for whatever
reason, nobody does.
In order to obtain MTBF (t)
for the general case, we would just calculate the
reciprocal of Lambda(t).
As described on the MTBF page, there
are two possibilities to distinguish between MTBF and MTTF.
One applies for redundant systems:
- MTBF = mean time between failure in
the steady state case
- MTTF = mean time to first failure, before the
systems enters steady state
There is a simple way to calculate
the mean time to first
failure, independent from case and state: We would simply
integrate R(t) over time:
Remember:
For the constant failure rate case we must set b to 1. We also "rename"
parameter a to lambda, and obtain:
As mentioned before, the most simplistic formula for
Availability A is just uptime divided by total time.
This is also called intrinsic
availability:
where MTBF = Mean time between
failure and MTTR =
mean time to repair.
This simple availability
definition
however doesn't account for preventive maintenance.
This does not mean that preventive
maintenance must be accounted for availability in any case. In fact it
is a matter of opinion whether or whether not preventive maintenance
should be accounted for availability.
The so called achieved availability
takes
into account preventive maintenance:
MTBM = Mean time between
maintenance
MMT=
Mean maintenance time
MMT includes mean time to repair,
mean preventive maintenence time, and probably more times where the
system is not in
operational state. However, it
does only include time where some kind of work is done. It therefore does not include delays,
logistics time and the like.
MTBM is actually a complete calendar
time, including all operational and non-operational times.
If you need also take
into account logistic time and other delays, then chose the operational
availability:
The
operational availability takes into account every kind of
non-operational time: corrective maintenance time (repair time, MTTR),
preventive maintenance time, logistics time, and other delays.
The most powerful tool for determining availability is the reliability block diagram.
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