Template:Alta exponential reliability function

The Reliability Function

The 1-parameter exponential reliability function is given by:

[math]\displaystyle{ R(T)={{e}^{-\lambda T}}={{e}^{-\tfrac{T}{m}}} }[/math]

This function is the complement of the exponential cumulative distribution function or:

[math]\displaystyle{ R(T)=1-Q(T)=1-\int_{0}^{T}f(T)dT }[/math]

and:

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