# Fail fraction and average fail rate FIT

The calculators below convert between fail fraction and average fail rate FIT given an operation time.

Fail fraction is probability of failure of a single unit or expected value of proportion of population failed at a given time. FIT is number of failures per 10^9 device-hours.

Say you are given a large number units (n) that have been operating over X hours. Of these n units, a certain number (y) have failed. This calculator extrapolates the Failures in Time (FIT) based on that failure rate. It will tell you how many failures per 10^9 device-hours you can expect given your current set of data.

### Purpose

Calculates AFR given your failure fraction and the time in operation for the units.

Equation

\[\begin{aligned} 10^9 * {(-1)}{\frac{ln(1-FailFraction)}{Hours}} \\ \end{aligned} \]

**FIT** - Failures in Time. One FIT equals one failure per billion hours device-hours of operation.

**Operation Hours** - Represets the number of hours the device is in use.

Average Fail Rate FIT to Fail Fraction

### Purpose

Calculates Average Failure Rate FIT between stated start and end times for the Lognormal Distribution given Shape and Scale (Characteristic Life) parameters.

Equation

\[\begin{aligned} 1 - e^{\frac{FIT * Hours}{10^9}} \\ \end{aligned} \]

**FIT** - Failures in Time. One FIT equals one failure per billion hours device-hours of operation.

**Operation Hours** - Represets the number of hours the device is in use.

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