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%.