MTBF and reliability calculator
MTBF is not a lifetime. It is the inverse of a failure rate, and a system with a hundred-year MTBF still fails 1% of the time in a year.
hours
hours
hours
Availability
99.984 00%
- Probability of surviving the mission
- 83.9289 %
- Probability all units survive
- 41.6445 %
- System MTBF
- 10 000 hours
- Expected failures per year
- 0.1753
- Downtime per year
- 1.402 hours
- Failure rate in FIT Failures per billion hours.
- 20 000.0
- Number of nines
- 3.796
Show the working
- Mean time between failures = 50 000
- Mean time to repair = 8
- Mission time = 8760
- Units in series = 5
- failure_rate = 1 / 50 000 = 0.000 02
- Failure rate in FIT = 0.000 02 * 1e9 = 20 000
- Availability = (50 000 + 8) > 0 ? 50 000/(50 000 + 8)*100 : 0 = 99.984
- Downtime per year = (100 - 99.984)/100 * 8766 = 1.402 34
- Probability of surviving the mission = exp(-8760/50 000) * 100 = 83.9289
- System MTBF = 5 > 0 ? 50 000/5 : 0 = 10 000
- Probability all units survive = exp(-8760 * 5/50 000) * 100 = 41.6445
- Expected failures per year = 8766 / 50 000 = 0.175 32
- Number of nines = 99.984 < 100 ? -log10(1 - 99.984/100) : 99 = 3.795 95
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- availability = MTBF / (MTBF + MTTR)
- reliability over time t = e^(-t/MTBF)
- failure rates in series add, so system MTBF = component MTBF / number of units
MTBF assumes a constant failure rate, which is only true during the flat part of the bathtub curve.
Five units each with a 50 000 hour MTBF give a system MTBF of 10 000 hours. Series reliability degrades fast.