The shown system has seven components with reliabilities R_A = 0.96, R_B = 0.92, R_C = 0.94, R_D = 0.89, R_E = 0.95, R_F = 0.88 and R_G = 0.90. Find system reliability to two decimals.
Assume independent failures. First parallel block has reliability $1-(1-R_A)(1-R_B)=0.9968$. The last block has E,F in series parallel to G, so reliability is $1-(1-0.95\times0.88)(1-0.90)=0.9836$. These blocks are in series with C and D: $R=0.9968(0.94)(0.89)(0.9836)=0.8202$. Rounded: **0.82**.
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