Template:Aaw rf: Difference between revisions

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If the parameter  <math>B</math>  is positive, then the reliability increases as stress decreases.
If the parameter  <math>B</math>  is positive, then the reliability increases as stress decreases.
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[[Image:ALTA6.7.png|center|250px|Behavior of the reliability function at different stress and constant parameter values.]]
[[Image:ALTA6.7.png|center|400px|Behavior of the reliability function at different stress and constant parameter values.]]
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Revision as of 15:30, 22 June 2012

Arrhenius-Weibull Reliability Function


The Arrhenius-Weibull reliability function is given by:


[math]\displaystyle{ R(T,V)={{e}^{-{{\left( \tfrac{T}{C\cdot {{e}^{\tfrac{B}{V}}}} \right)}^{\beta }}}} }[/math]


If the parameter [math]\displaystyle{ B }[/math] is positive, then the reliability increases as stress decreases.

Behavior of the reliability function at different stress and constant parameter values.



The behavior of the reliability function of the Weibull distribution for different values of [math]\displaystyle{ \beta }[/math] was illustrated here. In the case of the Arrhenius-Weibull model, however, the reliability is a function of stress also. A 3D plot such as the ones shown in the next figure is now needed to illustrate the effects of both the stress and [math]\displaystyle{ \beta . }[/math]


[math]\displaystyle{ }[/math]


Reliability function for [math]\displaystyle{ \Beta\lt 1 }[/math], [math]\displaystyle{ \Beta=1 }[/math], and [math]\displaystyle{ \Beta\gt 1 }[/math].