Template:Aaw stat prob sum

Conditional Reliability Function
The Arrhenius-Weibull conditional reliability function at a specified stress level is given by:


 * $$R(T,t,V)=\frac{R(T+t,V)}{R(T,V)}=\frac$$

or:


 * $$R(T,t,V)={{e}^{-\left[ {{\left( \tfrac{T+t}{C\cdot {{e}^{\tfrac{B}{V}}}} \right)}^{\beta }}-{{\left( \tfrac{T}{C\cdot {{e}^{\tfrac{B}{V}}}} \right)}^{\beta }} \right]}}$$

Reliable Life
For the Arrhenius-Weibull relationship, the reliable life, $${{t}_{R}}$$, of a unit for a specified reliability and starting the mission at age zero is given by:


 * $${{t}_{R}}=C\cdot {{e}^{\tfrac{B}{V}}}{{\left\{ -\ln \left[ R\left( {{t}_{R}},V \right) \right] \right\}}^{\tfrac{1}{\beta }}}$$

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

Arrhenius-Weibull Failure Rate Function
The Arrhenius-Weibull failure rate function, $$\lambda (T)$$, is given by:


 * $$\lambda \left( T,V \right)=\frac{f\left( T,V \right)}{R\left( T,V \right)}=\frac{\beta }{C\cdot {{e}^{\tfrac{B}{V}}}}{{\left( \frac{T}{C\cdot {{e}^{\tfrac{B}{V}}}} \right)}^{\beta -1}}$$