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Question 9.EX.12: Give the minimal path sets and the reliability function for ......

Give the minimal path sets and the reliability function for the structure in Figure 9.22.

9.22
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The minimal path sets are \{1,4\},\{1,5\},\{2,4\},\{2,5\},\{3,4\},\{3,5\}. With q_i=1-p_i, the reliability function is
\begin{aligned}r(\mathrm{p}) & =P \text { \{either of } 1,2 \text {, or } 3 \text { works }\} P\{\text { either of } 4 \text { or } 5 \text { works }\} \\& =\left(1-q_1 q_2 q_3\right)\left(1-q_4 q_5\right)\end{aligned}

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