﻿ Fatigue Life distribution

# Fatigue Life(time) distribution

Format: VoseFatigue(a, b, g, U)

Fatigue Life equations

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

##### Uses

The Fatigue Lifetime distribution was originally derived in Birnbaum and Saunders (1969) 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 from Central Limit Theorem. 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 suffering from fatigue. Other distributions in common use to model the lifetime of a devise are the Lognormal, Exponential and Weibull.

Lifetime distributions have their most obvious use in insurance in modeling the time until failure of a machine (e.g. turbine blades in a power station, cracks in a hull or wings). However, they are also the most obvious choices for time between events (insurance claims, shocks to a market, etc), particularly if you can see a parallel between the physical model from which the theory has been derived. One might, for example, see a parallel between the cracks scenario above and the commercial health of a company: each crack becomes some smallish incremental problem the company faces that impacts its goodwill, its financial stability, the strength of its leadership, etc. and the modeled time to 'failure' becomes the time until the company faces some huge resultant change (CEO resigns, major product recall, S&P demotion, etc).

(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 is more appropriate.

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

##### VoseFunctions for this distribution

VoseFatigue generates values from this distribution or calculates a percentile.

VoseFatigueObject constructs a distribution object for this distribution.

VoseFatigueProb returns the probability density or cumulative distribution function for this distribution.

VoseFatigueProb10 returns the log10 of the probability density or cumulative distribution function.

VoseFatigueFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution.

VoseFatigueFitObject constructs a distribution object of this distribution fitted to data.

VoseFatigueFitP returns the parameters of this distribution fitted to data.