Template:Ald rf

Reliability Function
For the lognormal distribution, the reliability for a mission of time $$T$$, starting at age 0, is given by:
 * $$R(T)=\mathop{}_{T}^{\infty }f(t)dt$$


 * or:


 * $$R(T)=\mathop{}_^{\infty }\frac{1}{{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{t-\overline{{{T}'}}}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}dt$$

There is no closed form solution for the lognormal reliability function. Solutions can be obtained via the use of standard normal tables.