A spacecraft navigation system consists of components of two types - A and B connected in a series-parallel arrangement, as in Figure 1.2. A B A B A B Figure 1.2 Illustration of series-parallel system The system will function as long as at least one component of each type functions. The probability that a type A component will function correctly throughout the planned lifetime of the spacecraft is 0.9; the corresponding probability for a component of type B is 0.8. Components may be assumed to fail independently of one another. The numbers of components of the two types may be varied in order to adjust the probability of failure of the navigation system. (a) Show that a requirement that the probability of failure of the entire system should be less than 1% may be met by using three components of each type (as in the diagram above). (b) If components of type A weigh 1 kg, while those of type B weigh 2 kg, what is the composition of the most reliable navigation system weighing 11 kg or less?
A spacecraft navigation system consists of components of two types - A and B connected in a series-parallel arrangement, as in Figure 1.2. A B A B A B Figure 1.2 Illustration of series-parallel system The system will function as long as at least one component of each type functions. The probability that a type A component will function correctly throughout the planned lifetime of the spacecraft is 0.9; the corresponding probability for a component of type B is 0.8. Components may be assumed to fail independently of one another. The numbers of components of the two types may be varied in order to adjust the probability of failure of the navigation system. (a) Show that a requirement that the probability of failure of the entire system should be less than 1% may be met by using three components of each type (as in the diagram above). (b) If components of type A weigh 1 kg, while those of type B weigh 2 kg, what is the composition of the most reliable navigation system weighing 11 kg or less?
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text:A spacecraft navigation system consists of components of two types - A and B connected in
a series-parallel arrangement, as in Figure 1.2.
A
B
A
B
A
B
Figure 1.2 Illustration of series-parallel system
The system will function as long as at least one component of each type functions. The
probability that a type A component will function correctly throughout the planned lifetime of
the spacecraft is 0.9; the corresponding probability for a component of type B is 0.8.
Components may be assumed to fail independently of one another.
The numbers of components of the two types may be varied in order to adjust the probability
of failure of the navigation system.
(a) Show that a requirement that the probability of failure of the entire system should be less
than 1% may be met by using three components of each type (as in the diagram above).
(b) If components of type A weigh 1kg, while those of type B weigh 2 kg, what is the
composition of the most reliable navigation system weighing 11 kg or less?
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