Reliability, risk analysis. Markov model. Nuclear, reliability, probability.

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6-6 A reactor has four identical, independent coolant loops. Each loop consists of three subsystems: the pump S ,, the electrical power S, to the pump, and the piping S; 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) A coolant loop is known to have failed. If there is 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. Calculate the probabilities that each subsystem failed, given that a loop has failed. (b) If all three subsystems function independently, and if all must function for a loop to operate, calculate the probability of a loop failure over the mission time of operation. (c) If each of the loops operates independently from the others, calcu- late the probability that at least three of the four will function for the entire mission time