6) For simplicity, assume that the successful firing of a rocket\'s propulsion s

Question

6) For simplicity, assume that the successful firing of a rocket's propulsion system depends on three components operating successfully; the controlling computer, the ignition system, and the fuel pump. Assume that the a) If the three components fail or survive independently, what is the probability of failure of the rocket the next b) Assuming independence between rocket firings, what is the probability that the rocket will successfully fire c) How does the result of part (a) change if the failure of the three components are assumed to be disjoint events, reliabilities of these three components on each firing of the rocket are 0.9995,0.9997, and 0.9998, respectively. time it is required? the next 100 times that it is required? rather than independent events?

Explanation / Answer

a)probability of failure =1-P( all components works ok) =1-0.9995*0.9997*0.9998=~ 0.001

b)probability that roket will successfully fire the next 100 times =(1-0.001)100 =0.9048

c)probability of failure =P( at least one of the component fails) =P( controlling computer fails+ignition system fails+fuel pump fails) =((1-0.9995)+(1-0.9997)+(1-0.9998)) =0.001

hence it will remain approximately the same due to high relaibility of individual components,

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