# The Maclaurin series and the Failure in Time (FIT)

Last edit: 07/08/2023

Mathematically, it can be shown that certain functions can be approximated by a series of other functions. In particular, ex can be developed as a so called Maclaurin series:

In case x <<1,

That means, the Reliability R(t) and Unreliability F(t) functions can be approximated to

The Failure Rate λ has a unit of inverse time: it is a common practice to use the unit of “failures per billion (109) hours.” This unit is known as FIT: Failure in Time.

#### Example: A component has a failure rate of 1000 FITs (10-6 h-1).

Question: what is its probability of failure after 105 hours (about 11 years) ?

By using the approximated formula

Answer: the probability of failure after approximately 11 years is 10%.

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