# 17-01-04 - 17.1.4(a Three components with reliabilities...

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17.1.4 (a) Three components with reliabilities r 1 := 0.920 r 2 := 0.950 r 3 := 0.975 are placed in series. A fourth component with reliability r 4 := 0.960 can be placed in parallel with any one of these three components. How should the fourth component be placed in order to maximize the overall system reliability? Calculate the parallel reliability of each possible combination: r 14 := 1 - 1 - r 1 ⋅ 1 - r 4 = .9968 r 24 := 1 - 1 - r 2 ⋅ 1 - r 4 = .998 r 34 := 1 - 1 - r 3 ⋅ 1 - r 4 = .999 Calculate the serial reliability of these resulting combinations: r 14 r 2 r 3 = .923286 r 1 r 24 r 3 = .895206 r 1 r 2 r 34 = .873126 Place the fourth component in parallel with the first one to maximize reliability. page 1

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(b) Does your answer to part (a) change if the value of r 4 changes? Component 4 placed in parallel with component 1: r := 1 - 1 - r 1 ⋅ 1 - r 4 r 2 r 3 r
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