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.
SOLUTION \blacktriangleright
Reliability for the middle path = R_2 \times R_3 = .975 \times .975 = .9506
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 \blacktriangleright 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 \blacktriangleright If reliability of all components is only .90, what is the new reliability? [Answer: .9981]
RELATED PROBLEMS \blacktriangleright 17.6, 17.8, 17.11
ACTIVE MODEL 17.3 This example is further illustrated in Active Model 17.3 in MyOMLab.