Template:Normal failure rate function

The Normal Failure Rate Function

The instantaneous normal failure rate is given by:

[math]\displaystyle{ \lambda (T)=\frac{f(T)}{R(T)}=\frac{\tfrac{1}{{{\sigma }_{T}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{T-\mu }{{{\sigma }_{T}}} \right)}^{2}}}}}{\int_{T}^{\infty }\tfrac{1}{{{\sigma }_{T}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{t-\mu }{{{\sigma }_{T}}} \right)}^{2}}}}dt} }[/math]