Calculate the reliability of the above system if components

Calculate the reliability of the above system if components A, B, C, D, and E function properly with probabilities 0.9, 0.8, 0.7, 0.6, and 0.5 respectively.

Solution

R1 (A and D in parallel)
R1 = 1 - ((1-Pa)*(1-Pd))
R1 = 1 - ((1-0.9)*(1-0.6)) = 0.96

R2 (B,C and E in parallel)
R2 = 1 - ((1-Pb)*(1-Pc)*(1-Pe))
R2 = 1 - ((1-0.8)*(1-0.7)*(1-0.5)) = 0.97

reliability of the system (R1 and R2 in series)
= R1 * R2
= 0.96 * 0.97
= 0.9312