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Question 17.9: Compute the reliability of an active redundant configuration......

Compute the reliability of an active redundant configuration system with two out of three units (all with identical reliability R) required for success.

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In this case, n = 3 and k = 2. The reliability for a k-out-of-n active redundancy reliability is obtained from Equation 17.40:

R_{2 \text { out of } 3}=\frac{3 !}{(1 !)(2 !)} R^2 Q^1+\frac{3 !}{(0 !)(3 !)} R^3 Q^0

R_{2 \ out \ of \ 3} = 3 R^{2}(1-R) + R^{3} \\ \boxed {\begin{aligned} Probability  that \\  two  units \ will \\ succeed \ and \\ one \ will \ fail \end{aligned}}   \boxed { \begin{aligned}Probability \\ that \ all \ three \\ units \ will \\ succeed \end{aligned}}

R_S(t)=\sum_{i=k}^n\binom{n}{i}[R(t)]^i[1-R(t)]^{n-i}, (17.40)

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