Template:Acb on reliability

Confidence Bounds on Reliability

The bounds on reliability for any given time, [math]\displaystyle{ T }[/math] , are estimated by:

[math]\displaystyle{ \begin{align} & {{R}_{U}}(T)= & {{e}^{-\tfrac{T}{{{m}_{U}}}}} \\ & {{R}_{L}}(T)= & {{e}^{-\tfrac{T}{{{m}_{L}}}}} \end{align} }[/math]

where [math]\displaystyle{ {{m}_{U}} }[/math] and [math]\displaystyle{ {{m}_{L}} }[/math] are estimated estimated by:

[math]\displaystyle{ \begin{align} & {{m}_{U}}= \widehat{m}\cdot {{e}^{\tfrac{{{K}_{\alpha }}\sqrt{Var(\widehat{m})}}{\widehat{m}}}} \\ & {{m}_{L}}= \widehat{m}\cdot {{e}^{-\tfrac{{{K}_{\alpha }}\sqrt{Var(\widehat{m})}}{\widehat{m}}}} \end{align} }[/math]