3. Consider the following system made up of functional components in parallel an
ID: 3043688 • Letter: 3
Question
3. Consider the following system made up of functional components in parallel and series.
3-1. What is the probability that the system operates?
3-2. (2 points) What is the probability that the system fails due to the components in series? Assume parallel components do not fail.
3-3. What is the probability that the system fails due to the components in parallel? Assume series components do not fail.
3-4. Compute and compare the probabilities that the system fails when the probability that component C1 functions is improved to a value of 0.99 and when the probability that component C2 functions is improved to a value of 0.89. Which improvement increases the system reliability more?
C2 0.85 C1 C4 0.95 0.90 C3 0.95Explanation / Answer
3.1) P(system operates) =P(C1 works)*P(at least one of C2 or C3 works)*P(C4 works)
=(0.95)*(1-(1-0.85)*(1-0.95))*(0.90)=0.848588
2) probability that the system fails due to the components in series =P(at least one of series component fails)
=1-P(none of series component) =1-0.95*0.90=0.145
3)probability that the system fails due to the components in parallel =P(both C2 and C3 fails) =(1-0.85)*(1-0.95)
=0.0075
4)
when C1 functions is improved to a value of 0.99:
P(system operates) =P(C1 works)*P(at least one of C2 or C3 works)*P(C4 works)
=(0.99)*(1-(1-0.85)*(1-0.95))*(0.90)=0.884318
when C2 functions is improved to a value of 0.89:
P(system operates) =P(C1 works)*P(at least one of C2 or C3 works)*P(C4 works)
=(0.99)*(1-(1-0.89)*(1-0.95))*(0.90)=0.850298
from abvoe we can see that improving C1 component relaibility increases the system reliability more
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