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    System reliability clarifications

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    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



    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