17-01-02 - 17.1.2 Calculate the reliability of the system...

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Unformatted text preview: 17.1.2 Calculate the reliability of the system diagram in Figure 17.9. r1 := 0.99 r2 := 0.90 r3 := 0.99 r4 := 0.95 r5 := 0.92 r45 := 1 - 1 - r4 1 - r5 r345 := r3 r45 = .98604 = .996 r2345 := 1 - 1 - r2 1 - r345 = .998604 r12345 := r1 r2345 = .988618 page 1 Problem 1 Consider the system of problem 17.1.2. However, now suppose that the components have the following constant failure rates: 1 := 0.01 2 := 0.10 3 := 0.01 4 := 0.05 5 := 0.08 Moreover, suppose that components 4 and 5 are configured as standby parallel, with component 4 the primary unit. Provide an expression for the overall system reliability as a function of time. - t 1 r1 t := e r1 t =e -t 100 r2 t := e - t 2 r2 t =e - t 10 r3 t := e - t 3 r3 t =e -t 100 r4 t := e - t 4 r4 t =e - t 20 f4 t := 4 e - t 4 r5 t := e - t 5 -2 t 25 r5 t = e page 2 t r45 t := r4 t + r5 t - s f4 s s 0 r45 t = e -2 t 25 3 t 100 8e - 5 3 r345 t := r3 t r45 t r345 t = e -9 t 100 3 t 100 8e - 5 3 r2345 t := 1 - 1 - r2 t 1 - r345 t r2345 t = e -19 t 100 13 t 100 8e - 5et 10 + 3e 9 t 100 - 8e 3 t 100 + 5 3 r12345 t := r1 t r2345 t r12345 t = - 5 13 e t 8e t 100 - 5et 10 + 3e 3 9 t 100 - 8e 3 t 100 + 5 expand r12345 t , e t - = 8 3 et 7 100 - 5 3 10 + e t 1 et 11 100 - 8 3 et 17 100 + 5 3 et 5 page 3 ...
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This note was uploaded on 05/12/2010 for the course ESI 6321 taught by Professor Josephgeunes during the Spring '07 term at University of Florida.

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