# AFR FIT for Lognormal Distribution

The Lognormal Distribution calculator is used to model cases where the causal degradation factors are multiplicative in nature.

This affects a model whereby the logs of times to “failure” (some predetermined threshold of the effect parameter being assessed) are characterized by a normal distribution.

### Purpose

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

Example mechanisms for semiconductors where the Lognormal Distribution model is commonly used include corrosion, electromigration, and some defect mechanisms.

Equations

\[\begin{aligned} \mathbf{Reliability} = 1 - \mathbf{NORMDIST} \left[ {ln \left( \frac{t_{hours}}{MTTF} \right), 0, \sigma} \right] \\ \end{aligned} \]

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

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

**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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