Template:Aae: Difference between revisions

Latest revision as of 23:57, 15 August 2012

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-==Arrhenius-Exponential==
+#REDIRECT [[Arrhenius_Relationship#Arrhenius-Exponential]]
-<br>
-The  <math>pdf</math>  of the 1-parameter exponential distribution is given by:
-<br>
-::<math>f(t)=\lambda {{e}^{-\lambda t}}</math>
-<br>
-It can be easily shown that the mean life for the 1-parameter exponential distribution (presented in detail [[Distributions used in Accelerated Testing#The Exponential Distribution|here]]) is given by:
-<br>
-::<math>\lambda =\frac{1}{m}</math>
-<br>
-thus:
-<br>
-::<math>f(t)=\frac{1}{m}{{e}^{-\tfrac{t}{m}}}</math>
-<br>
-The Arrhenius-exponential model  <math>pdf</math>  can then be obtained by setting  <math>m=L(V)</math>:
-<br>
-Therefore:
-<br>
-::<math>m=L(V)=C{{e}^{\tfrac{B}{V}}}</math>
-<br>
-Substituting for  <math>m</math> yields a  <math>pdf</math>  that is both a function of time and stress or:
-<br>
-::<math>f(t,V)=\frac{1}{C{{e}^{\tfrac{B}{V}}}}\cdot {{e}^{-\tfrac{1}{C{{e}^{\tfrac{B}{V}}}}\cdot t}}</math>
-{{aae stat prop sum}}
-===Parameter Estimation===
-{{aae mle}}