Template:Generalized gamma reliable life

Generalized Gamma Reliable Life

The reliable life, [math]\displaystyle{ {{T}_{R}} }[/math] , of a unit for a specified reliability, starting the mission at age zero, is given by:

[math]\displaystyle{ {{T}_{R}}=\left\{ \begin{array}{*{35}{l}} {{e}^{\mu +\tfrac{\sigma }{\lambda }\ln \left[ {{\lambda }^{2}}\Gamma _{I}^{-1}\left( 1-R,\tfrac{1}{{{\lambda }^{2}}} \right) \right]}}\text{ if }\lambda \gt 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}{{{\lambda }^{2}}} \right) \right]}}\text{ if }\lambda \lt 0 \\ \end{array} \right. }[/math]