Template:Logistic reliability function

The Logistic Reliability Function

The reliability for a mission of time [math]\displaystyle{ T }[/math] , starting at age 0, for the logistic distribution is determined by:

[math]\displaystyle{ R(T)=\int_{T}^{\infty }f(t)dt }[/math]

or:

[math]\displaystyle{ R(T)=\frac{1}{1+{{e}^{z}}} }[/math]

The unreliability function is:

[math]\displaystyle{ F=\frac{{{e}^{z}}}{1+{{e}^{z}}} }[/math]

where:

[math]\displaystyle{ z=\frac{T-\mu }{\sigma } }[/math]