Template:Exponential Reliability Function

The Exponential Reliability Function

The equation for the two-parameter exponential cumulative density function, or [math]\displaystyle{ cdf, }[/math] is given by:

[math]\displaystyle{ F(t)=Q(t)=1-{{e}^{-\lambda (t-\gamma )}} }[/math]

Recalling that the reliability function of a distribution is simply one minus the [math]\displaystyle{ cdf }[/math], the reliability function of the two-parameter exponential distribution is given by:

[math]\displaystyle{ R(t)=1-Q(t)=1-\int_{0}^{t-\gamma }f(x)dx }[/math]

[math]\displaystyle{ R(t)=1-\int_{0}^{t-\gamma }\lambda {{e}^{-\lambda x}}dx={{e}^{-\lambda (t-\gamma )}} }[/math]