The following system operates only if there is a path of fun

The following system operates only if there is a path of functional device from left to the right. The
probability that each device functions is as shown. What is the probability that the circuit operates?

The following system operates only if there is a path of functional device from left to the right. The probability that each device functions is as shown. What is the probability that the circuit operates? Assume 6 0.9 0.9 0.9 0.99- 0.98 0.97 0.95 independence 3

Solution

Lets divide the given part of circuit in 3 parts with part A containing loop with the devices 1,3,2,4 andPart B containing the loop with the devices 5 and 6 and Part C containing the device 7.

P(system operates) = P(A)*P(B)*P(C)

Now we have to find the values of P(A), P(B)

P(C) = 0.99

P(A) = P(1)*P(3)+P(2)*P(4) - P(1)P(3)P(2)P(4) = 0.98*0.97+0.9*0.9-0.98*0.97*0.9*0.9 = 0.99

P(B) = P(5) + P(6) - P(5)*P(6) = 0.9+0.95-0.95*0.9 = 0.995

Thus,

P(system operates) = 0.99*0.995*0.99 = 0.975