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%

Solution

P(AB) = (0.995)(0.987) = 0.9821

P(C) = 0.973

P(AB n C) = (0.995)(0.987)(0.973) = 0.9555

P(AB u C) = P(AB) + P(C) - P(AB n C)

= 0.9821 + 0.973 - 0.9555

= 0.99955