# AFR FIT for Weibull

The Weibull Distribution calculator is used to model cases where a “weakest link” constituent component leads to failure of the unit or system.

The Weibull Distribution is derived from Extreme Value theory. Example mechanisms for semiconductors where Weibull model is commonly used include Time Dependent Dielectric Breakdown (TDDB), solder joint thermal fatigue, or mechanical failure.

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### Purpose

Calculates Average Failure Rate FIT between stated start and end times for the Weibull Distribution given the Shape parameter.

### Equations

\begin{aligned} Reliability = e^{- \left({Time} / {Scale}\right) ^\beta} \\ \end{aligned}

\begin{aligned} \mathbf{Fail Probability \left(t_{end} - t_{start} \right)} = \frac{ \left( {\mathrm{Reliability}_{Start}} \right) - \left( {\mathrm{Reliability}_{End}} \right) }{\mathrm{Reliability}_{Start}} \\ \end{aligned}

\begin{aligned} \mathbf{AFR FIT} = 10^9 * \frac{ ln \left({\mathrm{Reliability}_{Start}} \right) - ln\left({\mathrm{Reliability}_{End}} \right) }{t_{end} - t_{start} } \\ \end{aligned}

β - Shape Parameter

Fail Probability - Conditional Failure Probability at time tend, given survival at time tstart.

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