# System reliability clarifications

Please see attachment for more clarification on question 1

1. Find the system reliability from the figure below.

2. Consider a system of 6 pumps of which at least 4 must function properly for system success. Each pump has an 85% reliability for the mission duration. Determine reliability of the system.

3. Suppose each engine has CFR = 0.0038074. Assuming 3-out-of 4 structure, find the followings:

a) The reliability of the system at a given time t

b) The system MTTF

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#### Solution Preview

Find the system reliability from the figure below.

First work out the reliability of components connected in series which have a combined

reliability defined by the product of the individual component reliabilities

Thus we define

R_12=R_1.R_2=0.9×0.8=0.72

R_345=R_3.R_4.R_5=0.8×0.8×0.9=0.576

Next combine the reliabilities of any parallel combinations. Observe in the above we

have one parallel combination that is R_12 and R_345 in parallel

And thus total reliability of this parallel combination is

R_12345=1-(1-R_12 )(1-R_345 )=1-(1-0.72)(1-0.576)=0.88128

Then we obtain a simplified reliability diagram

Then R_12345 in series with R_6 can be replaced by a single reliability R_123456determined

as the product of reliabilities

...

#### Solution Summary

Looking at system reliability by means of worked examples of component reliabilities in series and in parallel