For simplicity, assume that the successful firing of a rocket’s propulsion syste
ID: 2922053 • Letter: F
Question
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 reliabilities of these three components on each firing of the rocket are 0.9995, 0.9997, and 0.9998, respectively.
a) If the three components fail or survive independently, what is the probability of failure of the rocket the next time it is required?
b) Assuming independence between rocket firings, what is theprobability that the rocket will successfully fire the next 100 times that it is required?
c) How does the result of part (a) change if the failure of the three components are assumed to be disjoint events, rather than independent events?
Explanation / Answer
a)probability of failure of the rocket the next time it is required =1-P(none of the component failed)
=1-0.9995*0.9997*0.9998=0.001
b)probability that rocket successfully fires =(1-0.001)
hence probability that the rocket will successfully fire the next 100 times that it is required =(1-0.001)100 =0.9048
c)
for disjoint events probability of failure of the rocket the next time it is required =P(component 1 is failed+component 2 is failed+component 3 is failed) =(1-0.9995)+(1-0.9997)+(1-0.9998)=0.001