---
title: "Fatigue Life"
canonical: "https://modelassist.epixanalytics.com/space/EA/26575230/Fatigue%20Life"
format: markdown
---
No CrystalBall function

Fatigue(*a,b*,*g*)

[Fatigue Life equations](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26576155/)

 

The Fatigue Lifetime distribution is a right-skewed distribution bounded at *a*. *b* is a scale parameter while *g* controls its shape. Examples of the Fatigue Lifetime distribution are given below:

 

![image](media://ec89dad0-0786-4279-b395-dbcb81ca64ee)

### Uses

The Fatigue Lifetime distribution was originally derived in <span style="color: #ff0000">[Birnbaum and Saunders (1969)](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26579303)</span> as the failure of a structure due to the growth of cracks. The conceptual model had a single dominant crack appear and grow as the structure experiences repeated shock patterns up to the point that the crack is sufficiently long to cause failure. Assuming that the incremental growth of a crack with each shock follows the same distribution(1), that each incremental growth is an independent sample from that distribution(1), and that there are a large number of these small increases in length before failure, the total crack length will follow a [Normal distribution](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575246/) from [Central Limit Theorem](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26574953/). Birnbaum and Saunders determined the distribution of the number of these cycles necessary to cause failure. If the shocks occur more or less regularly in time, we can replace the probability that the structure will fail by a certain number of shocks with the probability it fails within a certain amount of time.

 

Thus, the Fatigue Lifetime distribution is used a great deal to model the [lifetime of a device](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575638/) suffering from fatigue. Other distributions in common use to model the lifetime of a devise are the [Lognormal](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575244/), [Exponential](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575227/) and [Weibull](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575257/).

 

(1) Big assumptions, so be careful in using this distribution despite its popularity. If the growth is likely to be proportional to the crack size, the [Lognormal distribution](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26576306/) is more appropriate.

### Comments

The fatigue life distribution is also commonly known as the *Birnbaum-Saunders distribution*. Fatigue(0,1,*g*) called the *standard fatigue life distribution*.

 

 

 

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