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* How to Calculate FITs and MTBF *
Since publishing this article last May in the Atlanta-based magazine TechLINKS, it has drawn more responses and requests than any other article. This business article is appropriate for anyone requiring an understanding of the quality, and reliability requirements for electronic components.
Calculating Failures In Time (FITs) is an important design step in predicting the likelihood of a failure, or the Mean Time Between Failures (MTBF).
Equation - Acceleration Models
The three variables in the Arrhenius model are the Use (T1) and Test (T2) temperature in degree Kelvin, and the Activation Energy (EA) in eV. Selecting the appropriate Activation Energy for the failure mode being modeled is important, and values can be found in publications from suppliers, or publications like Telcordia GR-486 CORE, or MIL HDBK 217. It can be seen from the Arrhenius equation that the Acceleration coefficient (AF), changes significantly with small changes in Activation energy (EA), so that value must be chosen with care.
The exponential distribution model is used in this example, and many other applications in reliability. A unique value of the exponential distribution for reliability use is that it is the only distribution which has a constant failure rate λ, which is also the reciprocal of the MTBF. With the characteristic bathtub curve, we think of the first part as early failures, the middle as the intrinsic failures, or normal life expectancy, and the end as wear-out failures. The long, flat middle section, or normal life expectancy can be modeled as an exponential distribution, where we can then view those failures as random failures, occurring at a constant rate.
The example below uses the Arrhenius equation and Chi-Square distribution, respectively:
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