MTBF | Thomas Reiter
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    • MTBF Calculation
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    • Reliability
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    • MTBF
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    • Functional Safety
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    • FMEA & FMECA
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    • Reliability Block Diagrams
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    • Fault Tree Analysis
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    • Event Tree Analysis
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    • Markov Analysis
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    • Weibull Analysis
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MTBF, MTTF & Availability

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1. MTTF & MTBF

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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:

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:

MTTF = integral R(t)
Remember:
 Weibull

For the constant failure rate case we must set b to 1. We also "rename" parameter a to lambda, and obtain:





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2. Availability

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As mentioned before, the most simplistic formula for Availability A is just uptime divided by total time.
This is also called intrinsic availability: 
    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:
  Achieved Availability
 
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:
  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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