This system works if A and B work or C works Find P AB U C

This system works if A and B work or C works

Find P( AB U C) .

Consider a system with three components Units 1 and 2 are connected in series and Unit 3 is connected in parallel with the first two as shown in the next figure What is the reliability of the system if R1 = 99.5%, R2 = 98.7% and R3 = 97.3% This system works if A and B work or C works Find P( AB U C) .

Solution

P(A) = 99.5% = 0.995

P(B) = 98.7% = 0.987

P(C) = 97.3% = 0.973

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P(AB or C) = P(A)*P(B) + P(C) - P(A)P(B)P(C)

= 0.995*0.987 + 0.973 - 0.995*0.987*0.973

= 0.9995