# 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.

### Purpose

Calculates Average Failure Rate FIT between stated start and end times for the Lognormal Distribution given Shape and Median Time To Failure (MTTF) parameters.

Equations

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

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

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

**σ **- Shape Parameter

**MTTF** - Median Time to Failure

**Fail Probability** - Conditional Failure Probability at time t end, given survival at time t start

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