Question: A reactor has four identical, independent coolant loops. Each loop consists of three subsystems: the pump S1, the electrical power S2 to the pump, and the piping S3 that circulates the coolant. Over the mission time for operation, the probability of a pump failure is 0.2, of electrical power failure is 0.05, and of pipe failure is 0.001.Assume there is no repair during the operating period of interest.

(a) Given that a coolant loop has failed, calculate the probabilities that each subsystem failed if it is known that with an electrical power failure the loop will certainly fail, but only 60% of the pump failures cause a loop failure, and only 40% of the pipe failures cause a loop failure.

(b) If all three subsystems function independently, determine the probability of a loop failure over the mission time of operation.

(c) If each of the loops operates independently from the others, calculate the probability that at least three of the four will function for the entire mission time.