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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?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 1EQ: 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed...
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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?
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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