Solutions - 5090-03

Let $T$ denote the top branch (A series B) and $L$ denote the bottom branch (C parallel D).

(1) Compute the top-branch reliability:

$$P[T]=P[A]\cdot P[B]=0.9\cdot 0.95=0.855$$

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(2) Compute the bottom-branch reliability:

$$\begin{array}{c}P[L^c]=P[C^c]\cdot P[D^c]\\ \\ \gg \gg 0.1\cdot 0.2\gg \gg 0.02\\ \\ \gg \gg P[L]=0.98\end{array}$$

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(3) Combine (T and L are in parallel):

$$\begin{array}{c}P[\text{system fails}]=P[T^c]\cdot P[L^c]\\ \\ \gg \gg 0.145\cdot 0.02\gg \gg 0.0029\\ \\ \gg \gg P[\text{system works}]=1-0.0029\gg \gg 0.9971\end{array}$$