MTBF is the abbreviation for Mean Time Between Failures. MTBF is an indicator of the reliability of a reparable product or system. It measures the rate of random failures, excluding systematic failures due, for example, to design errors (e.g., software errors) or manufacturing defects (products at the start of their life cycle), and excluding wear and tear due to use (products at the end of their life cycle).
MTBF is usually expressed in number of hours. The higher the MTBF, the higher the reliability of the product or system.
An MTBF value can only be assigned for a given use and environment. For example, the MTBF of a given product for operation between -20°C and +70°C will be different compared to when the product is used indoors at 20°C or outdoors at 70°C.
MTBF Calculations
When a system consists of multiple components, the failure rates of each component must be totaled, assuming that the failure of a single component will cause system failure.
MTBF = 1/(Σ of the failure rate of each system component).
Note: This does not apply to complex systems (for example, redundant systems) where the failure rates are not constant.
The probability (P) that the product will function during time T prior to a failure is equal to
P(T) = e ^{(-T/MTBF)}
Example 1: Oldham System MX 43, 4-channel version, 24 V power supply, 25°C usage temperature
MTBF = 174,805 hours (19.95 years)
The probability that the system will operate 5 years prior to a failure is P = e^{(-5/19,95)} = 77.8%.
Example 2: Oldham OLCT 100 gas detector for detecting explosive gas.
This detector was certified as SIL2 by a certified entity. The reliability data are the following:
- Dangerous un-detected failure rate (λ_{du}) = 189.10^{-9 }per hour
- Proportion of non-dangerous failures (SFF) = 92.9%
SFF = 1 – ( λ_{du}/Σ of the failure rate)
therefore Σ of the failure rate = 2.66x10^{-6} per hour = 0.0233 per year
and MTBF = 1/Σ of the failure rate = 42.9 years.
The probability that the detector will operate 4 years (average life of a cell for detecting explosive gas) prior to a failure is 91.1%.
MTBF also includes the time necessary to diagnose the failure, supply the replacement parts and resume operation (these times correspond to the MTTR: Mean Time To Repair). The MTTR for the OLCT100 is 24 hours and is negligible for 42.9 years.