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==Arrhenius-Weibull==
#REDIRECT [[Arrhenius_Relationship]]
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The  <math>pdf</math>  for the 2-parameter Weibull distribution is given by:
 
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::{{weibull2pdf}}
 
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The scale parameter (or characteristic life) of the Weibull distribution is  <math>\eta </math> .
 
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The Arrhenius-Weibull model pdf can then be obtained by setting  <math>\eta =L(V)</math>:
 
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::<math>\eta =L(V)=C\cdot {{e}^{\tfrac{B}{V}}}</math>
 
 
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and substituting for  <math>\eta </math>  in the 2-parameter Weibull distribution equation:
 
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::<math>f(t,V)=\frac{\beta }{C\cdot {{e}^{\tfrac{B}{V}}}}{{\left( \frac{t}{C\cdot {{e}^{\tfrac{B}{V}}}} \right)}^{\beta -1}}{{e}^{-{{\left( \tfrac{t}{C\cdot {{e}^{\tfrac{B}{V}}}} \right)}^{\beta }}}}</math>
 
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An illustration of the  <math>pdf</math>  for different stresses is shown in the next figure.  As expected, the  <math>pdf</math>  at lower stress levels is more stretched to the right, with a higher scale parameter, while its shape remains the same (the shape parameter is approximately 3). This behavior is observed when the parameter  <math>B</math>  of the Arrhenius model is positive.
 
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[[Image:ALTA6.6.gif|thumb|center|300px|Behavior of the probability density function at different stresses and with the parameters held constant.]]
 
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The advantage of using the Weibull distribution as the life distribution lies in its flexibility to assume different shapes. The Weibull distribution is presented in greater detail [[Distributions used in Accelerated Testing#The Weibull Distribution|here]].
 
{{aaw stat prob sum}}
 
===Parameter Estimation===
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{{aaw mle}}

Latest revision as of 07:26, 8 August 2012

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