# Weibull distribution

In order to create a model of the failure distribution of a product, it is necessary to be able to model multiple types of failure:

Therefore, considerable shape flexibility is necessary. The distribution primarily used for this is the Weibull distribution because it allows for a greater shape variability.

Because of its flexibility, the Weibull distribution makes the modelling of the behaviour of numerous types of failure possible, such as

- Components' resistance to rupture or the effort required to wear out metals.
- The failure time of an electronic component.
- The failure time for articles used outdoors such as pneumatic automobiles.
- Systems that fail when the weakest component in the system contains a defect.
The Weibull distribution also supports the modelling of the behaviour of different lifespan situations for one component.
The function of the Weibull distribution is as follows:

It is composed of 3 parameters:

- β - shape parameter
- θ - scale parameter
- δ - delay parameter

## β, shape parameter :

It makes adaptation of the distribution's shape possible to place it as close as possible to the observed failure rate:

*β = 1: The failure rate is constant (λ constant)*

*β > 1: The failure rate increases with time (λ increases - product's end of life)*

*β < 1: The failure rate decreases with time (λ decreases - infant failure)*
## θ, scale parameter :

The θ parameter makes it possible to adjust the scale of the distribution law to the scale of the observed problem, for example:

Failure appears around t = 90.4

Failure appears around t = 904

## δ, delay parameter:

The δ parameter makes it possible to move the distribution law by one parameter δ

*Β = 3,6 – θ = 100, δ = 0*
Failure appears around t = 90.4

*Β = 3,6 – θ = 100, δ = 100*
Failure appears around t = 190.4