Template:Lognormal distribution failure rate function

The Lognormal Failure Rate Function

The lognormal failure rate is given by:

[math]\displaystyle{ \lambda (T)=\frac{f(T)}{R(T)}=\frac{\tfrac{1}{T\cdot {{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{(\tfrac{{T}'-{\mu }'}{{{\sigma }_{{{T}'}}}})}^{2}}}}}{\int_{{{T}'}}^{\infty }\tfrac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{(\tfrac{t-{\mu }'}{{{\sigma }_{{{T}'}}}})}^{2}}}}dt} }[/math]

As with the reliability equations, standard normal tables will be required to solve for this function.