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Question 17.10: Consider a system that has eight components and the system w......

Consider a system that has eight components and the system will work if at least any five of the eight components work (5-out-of-8 system). Each component has a reliability of 0.87 for a given period. Find the reliability of the system.

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R_S=\sum_{i=k}^n\binom{n}{i} R^i(1-R)^{n-i}=\sum_{i=5}^n\binom{8}{i} R^i(1-R)^{8-i} \\ =\binom{8}{5} 0.87^5(0.13)^3+\binom{8}{6} 0.87^6(0.13)^2+\binom{8}{7} 0.87^7(0.13)^1+\binom{8}{8} 0.87^8(0.13)^0 \\ =56(0.001095)+28(0.007328)+8(0.049043)+0.328212 \\ =0.06132+0.205192+0.392345+0.328212=0.98707

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