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(T)dT }[/math]

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