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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].