RELIABILITY WITH PARALLEL REDUNDANCY. A new iPad design that is more reliable because of its parallel circuits is shown below. What is its reliability?

APPROACH $\blacktriangleright$ Identify the reliability of each path, then compute the likelihood of needing additional paths (likelihood of failure), and finally subtract the product of those failures from 1.

Question

RELIABILITY WITH PARALLEL REDUNDANCY. A new iPad design that is more reliable because of its parallel circuits is shown below. What is its reliability?

APPROACH [latex]\blacktriangleright[/latex] Identify the reliability of each path, then compute the likelihood of needing additional paths (likelihood of failure), and finally subtract the product of those failures from 1.

Accepted Answer

SOLUTION [latex]\blacktriangleright[/latex]
Reliability for the middle path = [latex]R_2 imes R_3 = .975 imes .975 = .9506[/latex]
Then determine the probability of failure for all 3 paths = (1 - 0.95) × (1 - .9506) × (1 - 0.95)
= (.05) × (.0494) × (.05) = .00012
Therefore the reliability of the new design is 1 minus the probability of failures, or
= 1 - .00012 = .99988

INSIGHT [latex]\blacktriangleright[/latex] Even in a system where no component has reliability over .975, the parallel design increases reliability to over .999. Parallel paths can add substantially to reliability.
LEARNING EXERCISE [latex]\blacktriangleright[/latex] If reliability of all components is only .90, what is the new reliability? [Answer: .9981]
RELATED PROBLEMS [latex]\blacktriangleright[/latex] 17.6, 17.8, 17.11
ACTIVE MODEL 17.3 This example is further illustrated in Active Model 17.3 in MyOMLab.

Question 17.EX.4: RELIABILITY WITH PARALLEL REDUNDANCY. A new iPad design that...

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