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In reliability and functional safety, FIT (Failures In Time) expresses the expected number of failures per \(10^9\) device-hours. Core relationships:

From failure rate:
\[ \text{FIT} = \lambda \times 10^9 \quad\Rightarrow\quad \lambda = \frac{\text{FIT}}{10^9} \; [\text{h}^{-1}] \]

From field data:
\[ \text{FIT} = \frac{N_{\text{fail}}}{H_{\text{total}}}\times 10^9 \] where \(N_{\text{fail}}\) is the observed failures and \(H_{\text{total}}\) is total device-hours.

Mean Time To Failure (MTTF):
\[ \text{MTTF} = \frac{1}{\lambda} = \frac{10^9}{\text{FIT}} \; [\text{hours}] \]

Series combination (independent components):
\[ \text{FIT}_{\text{total}} = \sum_i \text{FIT}_i \]

Optional dangerous fraction and PFH:
If a fraction \(f_d\) of failures is dangerous, then \[ \text{FIT}_{\text{d}} = f_d \cdot \text{FIT}, \qquad \text{PFH}_\text{d} = \frac{\text{FIT}_{\text{d}}}{10^9} \; [\text{per hour}] \]

Assumptions: constant failure rate (exponential model), independent components for series summation, and steady-state operation. Confidence intervals from statistical models (e.g., Chi-square) are not included in this basic version.

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