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:


 * $$R(t)=1-Q(t)=1-\int_{0}^{t-\gamma }f(x)dx$$


 * $$R(t)=1-\int_{0}^{t-\gamma }\lambda {{e}^{-\lambda x}}dx={{e}^{-\lambda (t-\gamma )}}$$