3. Consider the following system made up of functional components in parallel an

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?

Explanation / 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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