Template:Lambda-beta parameter relationship

Lambda - Beta Parameter Relationship
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 $$\beta $$  and  $$\eta $$  is:


 * $$MTTF=\eta \cdot \Gamma \left( 1+\frac{1}{\beta } \right)$$

The parameter lambda is defined as:


 * $$\lambda =\frac{1}$$

Using Eqn. (lambda eta relationship), the MTTF relationship shown in Eqn. (Weibull MTTF) becomes:


 * $$MTB{{F}_{B}}=\frac{\Gamma \left( 1+\tfrac{1}{\beta } \right)}$$

Or, in terms of failure intensity:


 * $${{\lambda }_{B}}=\frac{\Gamma \left( 1+\tfrac{1}{\beta } \right)}$$