A commercial jet aircraft has four engines. For an aircraft in flight to land safely, at least two engines should be in working condition. Each engine has an independent reliability of p=92%. a. What is the probability that an aircraft in flight can land safely? b. If the probability of landing safely must be at least 99.5%, what is the mini- mum value for p? Repeat the question for probability of landing safely to be 99.9%. c. If the reliability cannot be improved beyond 92% but the number of engines in a plane can be increased, what is the minimum number of engines that would achieve at least 99.5% probability of landing safely? Repeat for 99.9% probability.
A commercial jet aircraft has four engines. For an aircraft in flight to land
safely, at least two engines should be in working condition. Each engine has an independent
reliability of p=92%.
a. What is the
b. If the probability of landing safely must be at least 99.5%, what is the mini-
mum value for p? Repeat the question for probability of landing safely to
be 99.9%.
c. If the reliability cannot be improved beyond 92% but the number of
engines in a plane can be increased, what is the minimum number of
engines that would achieve at least 99.5% probability of landing safely?
Repeat for 99.9% probability.
d. One would certainly desire 99.9% probability of landing safely. Looking
at the answers to (b) and (c ), what would you say is a better approach
to safety, increasing the number of engines or increasing the reliability of
each engine?
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