Cheetsheet

Probability Logic Table

VotingFormulaComment
1oo1PASingle element system
1oo2PAPBBoth devices fail
2oo2PA + PB – PAPBEither device fails
1oo3PAPBPCAll devices must fail
2oo3PAPB + PAPC + PBPC – 2PAPBPCAny two devices must fail
3oo3PA + PB + PC – PAPB – PAPC – PBPC + PAPBPCAny device fails

PFD Equations

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

VotingPFDPFD Avg
1oo11eλt1 - e^{-\lambda t}1+eλT1λT1 + \frac{e^{-\lambda T}-1}{\lambda T}
1oo212eλt+e2λt1 - 2e^{-\lambda t} + e^{-2\lambda t}1+2eλT2λT+1e2λT2λT1 + \frac{2e^{-\lambda T}-2}{\lambda T} + \frac{1-e^{-2\lambda T}}{2\lambda T}
2oo21e2λt1 - e^{-2\lambda t}1+e2λT12λT1 + \frac{e^{-2\lambda T}-1}{2\lambda T}
1oo313eλt+3e2λte3λt1 - 3 e^{- \lambda t} + 3 e^{- 2 \lambda t} - e^{- 3 \lambda t}1116λT+3eλTλT3e2λT2λT+e3λT3λT1 - \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}
2oo313e2λt+2e3λt1 - 3 e^{- 2 \lambda t} + 2 e^{- 3 \lambda t}156λT+3e2λT2λT2e3λT3λT1 - \frac{5}{6 \lambda T} + \frac{3 e^{- 2 \lambda T}}{2 \lambda T} - \frac{2 e^{- 3 \lambda T}}{3 \lambda T}
3oo31e3λt1 - e^{- 3 \lambda t}113λT+e3λT3λT1 - \frac{1}{3 \lambda T} + \frac{e^{- 3 \lambda T}}{3 \lambda T}

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