In airline applications, failure of a component can result
in catastrophe. As a result, many airline components utilize
something called triple modular redundancy. This means that a
critical component has two backup components that may be utilized
should the initial component fail. Suppose a certain critical
airline component has a probability of failure
of 0.038 and the system that utilizes the component is
part of a triple modular redundancy.
(a) What is the probability that the system does
not fail?
(b) Engineers decide to the probability of failure is too high
for this system. Use trial and error to determine the minimum
number of components that should be included in the system to
result in a system that has greater than a 0.99999999 probability
of not failing.