OpenSpecEngineering

Converts between the mean time between failures (MTBF) and the failure rate of a repairable item, and gives its failure rate in FIT, its inherent availability, its reliability over a mission time and the number of failures to expect in that time. Reliability, maintenance and design engineers use it to set spares levels, to compare equipment and to feed a system reliability model [1]–[3].

Equations

λ = 1 / MTBF     FIT = 10⁹·λ

A_i = MTBF / (MTBF + MTTR)

R(t) = e^−t/MTBF     Expected failures = λ·t

λ is the failure rate in failures per operating hour, and FIT is failures per billion hours, the unit used for electronic parts [3]. MTTR is the mean time to repair: the hands-on time to diagnose, fix and test, all in hours. A_i is the inherent availability, the share of time the item is up when only corrective repair counts [1], [2]. t is the mission time, and R(t) is the probability of running that long with no failure. The page assumes a constant failure rate, so failures follow the exponential distribution.

Limits and common mistakes

• A constant failure rate fits the useful-life part of the bathtub curve. It doesn’t fit early failures or wear-out; for those use the Weibull Reliability calculator.
• MTBF is not a life. An item with an MTBF of 15,000 hours has only a 37 % chance of running that long without a failure.
• Inherent availability leaves out waiting for parts and people, and planned maintenance. The availability seen on the floor (operational availability) is lower.
• Use operating hours, not calendar hours, unless the item runs around the clock.

Worked example

A process pump that runs around the clock has an MTBF of 15,000 hours, and a repair takes 24 hours on average. How available is it, and how likely is it to run a full year (8,760 hours) without a failure?

1. Choose Reliability Input MTBF (hours) and enter MTBF (hours) 15000.
2. Enter Mean Time to Repair (MTTR, hours) 24.
3. Enter Mission Time (t, hours) 8760 and press Solve. The Solution shows: MTBF: 15,000 hr
   Failure rate λ: 6.66667e-5 per hr
   FIT (failures per 10⁹ hr): 66,666.7 FIT
   Inherent availability Ai: 99.8403 %
   Reliability at mission time R(t): 0.557663
   Expected failures over mission time: 0.584

Check: 8,760 / 15,000 = 0.584 expected failures, and e^−0.584 = 0.558. The pump is up 15,000 of every 15,024 hours, or 99.84 %. There is a 44 % chance of at least one repair in the year, so keep a seal kit on the shelf.