Template:Aw crf

The Conditional Reliability Function

The Weibull conditional reliability function is given by:

[math]\displaystyle{ R(T,t)=\frac{R(T+t)}{R(T)}=\frac{{{e}^{-{{\left( \tfrac{T+t}{\eta } \right)}^{\beta }}}}}{{{e}^{-{{\left( \tfrac{T}{\eta } \right)}^{\beta }}}}} }[/math]

or:

[math]\displaystyle{ R(T,t)={{e}^{-\left[ {{\left( \tfrac{T+t}{\eta } \right)}^{\beta }}-{{\left( \tfrac{T}{\eta } \right)}^{\beta }} \right]}} }[/math]

The above equation gives the reliability for a new mission of [math]\displaystyle{ t }[/math] duration, having already accumulated [math]\displaystyle{ T }[/math] hours of operation up to the start of this new mission, and the units are checked out to assure that they will start the next mission successfully. (It is called conditional because you can calculate the reliability of a new mission based on the fact that the unit(s) already accumulated [math]\displaystyle{ T }[/math] hours of operation successfully.)