Cheetsheet

Probability Logic Table

PFD equations (not simplified) assuming all devices in the voting scheme have the same lambda:

Voting	PFD	PFD Avg
1oo1	$1 - e^{-\lambda t}$	$1 + \frac{e^{-\lambda T}-1}{\lambda T}$
1oo2	$1 - 2e^{-\lambda t} + e^{-2\lambda t}$	$1 + \frac{2e^{-\lambda T}-2}{\lambda T} + \frac{1-e^{-2\lambda T}}{2\lambda T}$
2oo2	$1 - e^{-2\lambda t}$	$1 + \frac{e^{-2\lambda T}-1}{2\lambda T}$
1oo3	$1 - 3 e^{- \lambda t} + 3 e^{- 2 \lambda t} - e^{- 3 \lambda t}$	$1 - \frac{11}{6 \lambda T} + \frac{3 e^{- \lambda T}}{\lambda T} - \frac{3 e^{- 2 \lambda T}}{2 \lambda T} + \frac{e^{- 3 \lambda T}}{3 \lambda T}$
2oo3	$1 - 3 e^{- 2 \lambda t} + 2 e^{- 3 \lambda t}$	$1 - \frac{5}{6 \lambda T} + \frac{3 e^{- 2 \lambda T}}{2 \lambda T} - \frac{2 e^{- 3 \lambda T}}{3 \lambda T}$
3oo3	$1 - e^{- 3 \lambda t}$	$1 - \frac{1}{3 \lambda T} + \frac{e^{- 3 \lambda T}}{3 \lambda T}$