Template:Aw reliable life

The Reliable Life

For the 2-parameter Weibull distribution, 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}}=\eta \cdot {{\left\{ -\ln \left[ R\left( {{T}_{R}} \right) \right] \right\}}^{\tfrac{1}{\beta }}} }[/math]

This is the life for which the unit will function successfully with a reliability of [math]\displaystyle{ R({{T}_{R}}) }[/math] . If [math]\displaystyle{ R({{T}_{R}})=0.50 }[/math] then [math]\displaystyle{ {{T}_{R}}=\breve{T} }[/math], the median life, or the life by which half of the units will survive.