Template:Generalized gamma reliable life

Generalized Gamma Reliable Life
The reliable life, $${{T}_{R}}$$, of a unit for a specified reliability, starting the mission at age zero, is given by:


 * $${{T}_{R}}=\left\{ \begin{array}{*{35}{l}}

{{e}^{\mu +\tfrac{\sigma }{\lambda }\ln \left[ {{\lambda }^{2}}\Gamma _{I}^{-1}\left( 1-R,\tfrac{1} \right) \right]}}\text{ if }\lambda >0  \\ {{\Phi }^{-1}}(1-R)\text{                 if }\lambda =0  \\ {{e}^{\mu +\tfrac{\sigma }{\lambda }\ln \left[ {{\lambda }^{2}}\Gamma _{I}^{-1}\left( R,\tfrac{1} \right) \right]}}\text{    if }\lambda <0  \\ \end{array} \right.$$