Weibull law

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:

Exemple de loi

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:

Loi de weibull

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:

Wiebull beta = 1

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

wiebull beta = 2.6

β > 1: The failure rate increases with time (λ increases – product’s end of life)

Weibull beta = 0.8

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:

wiebull beta = 2.6

Failure appears around t = 90.4

Wiebull theta = 1000

Failure appears around t = 90.4

δ, delay parameter :

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

wiebull beta = 2.6

Β = 3,6 – θ = 100, δ = 0

Failure appears around t = 90.4

Weibull delta = 100

Β = 3,6 – θ = 100, δ = 100

Failure appears around t = 190.4