Template:Lambda-beta parameter relationship: Difference between revisions

Latest revision as of 01:48, 27 August 2012

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-====Lambda - Beta Parameter Relationship====
+#REDIRECT [[Reliability_Growth_Planning#Lambda_-_Beta_Parameter_Relationship]]
-<br>
-Under the Crow-AMSAA (NHPP) model, the time to first failure is a Weibull random variable. The MTTF of a Weibull distributed random variable with parameters  <math>\beta </math>  and  <math>\eta </math>  is:
-::<math>MTTF=\eta \cdot \Gamma \left( 1+\frac{1}{\beta } \right)</math>
-The parameter lambda is defined as:
-::<math>\lambda =\frac{1}{{{\eta }^{\beta }}}</math>
-Using Eqn. (lambda eta relationship), the MTTF relationship shown in Eqn. (Weibull MTTF) becomes:
-::<math>MTB{{F}_{B}}=\frac{\Gamma \left( 1+\tfrac{1}{\beta } \right)}{{{\lambda }^{\left( \tfrac{1}{\beta } \right)}}}</math>
-Or, in terms of failure intensity:
-::<math>{{\lambda }_{B}}=\frac{{{\lambda }^{\left( \tfrac{1}{\beta } \right)}}}{\Gamma \left( 1+\tfrac{1}{\beta } \right)}</math>