Template:Exponential Reliability Function

The Exponential Reliability Function
The equation for the two-parameter exponential cumulative density function, or $$cdf,$$ is given by:


 * $$F(T)=Q(T)=1-{{e}^{-\lambda (T-\gamma )}}$$

Recalling that the reliability function of a distribution is simply one minus the $$cdf$$, the reliability function of the two-parameter exponential distribution is given by:


 * $$R(T)=1-Q(T)=1-\int_{0}^{T-\gamma }f(T)dT$$


 * $$R(T)=1-\int_{0}^{T-\gamma }\lambda {{e}^{-\lambda T}}dT={{e}^{-\lambda (T-\gamma )}}$$