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 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 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?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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