Benutzerhandbuch Menü

Benutzerhandbuch

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:
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:
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 = 904

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

Eine Komplettlösung für Industrie 4.0

8 statistische Module

trial

Versuch

0

30 Tage

Testen Sie es kostenlos

APC

SPC

Kontrolle

Analyse

check

30 Tage

check

Alle Funktionen von Ellistat

check

1 Benutzer

Technische Unterstützung und Wartung inbegriffen

student

Student

0

1 Jahr

Zur Kasse

Analyse

check

1 Jahr

check

Alle Funktionen von Ellistat

check

1 Benutzer

check

Lizenz für Studenten, die über einen gültigen Studentenausweis verfügen

Technische Unterstützung und Wartung inbegriffen

standard

Standard

49

pro Benutzer pro Monat

Zur Kasse

Analyse

check

Lizenz wird alle zwei Monate erneuert

check

Alle Funktionen von Ellistat

check

Unbegrenzter Benutzer

check

Technische Unterstützung und Wartung inbegriffen