Problem 4 Consider the system of components connected as depicted below. The sys

Question

Problem 4 Consider the system of components connected as depicted below. The system can be thought of as being comprised of two subsystems: one with components A and B, and the other with components C and D. Components A and B are connected in parallel, therefore that subsystem works iff either A or B works. Since C and D are connected in series, that subsystem works iff both C and D work. Components work independent of each other (that is, operation/failure of one component doesn't influence the operation/failure of another). If event A is defined as "component A works" and so on, then P(A)-P(B) = P(C) = P(D) 0.90. Calculate P(system works) as a function of the P() notation. Calculate the quantity for P(system works). a. b.

Explanation / Answer

P(subsystem AB works) =P(at least one of A or B works) =P(A)+P(B)-P(A)*P(B)

P(subsysem CD works =P(both C and D works) =P(C)*P(D)

therefore

a) P(system works) =1-P(none of AB and CD works) =1-(1-(P(A)+P(B)-P(A)*P(B)))*(1-P(C)*P(D))

n)P(system works)=1-(1-(0.9+0.9-0.9*0.9))*(1-0.9*0.9)= 0.9981

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