Question 1: The following system is designed to deliver emergency cooling to a nuclear reactor.

In the event of an accident the protection system delivers an actuation signal to the two identical pumps and the four identical valves. The pumps then start up, the valves open, and liquid coolant is delivered to the reactor. The following failure probabilities are found to be significant:

p_ps = 10^-5 the probability that the protection system will not deliver a signal to the pump and valve actuators.

p_p = 2 X 10^-2 the probability that a pump will fail to start when the actuation signal is received.

p_v, = 10^-1 the probability that a valve will fail to open when the actuation signal is received.

p_r = 0.5 X 10^-5 the probability that the reservoir will be empty at the time of the accident.

(a) Draw a fault tree for the failure of the system to deliver any coolant to the primary system in the event of an accident.

(b) Evaluate the probability that such a failure will take place in the event of an accident.

Question 2:

A device has a constant failure rate of 0.7/year.

(a) What is the probability that the device will fail during the second year of operation?

(b) If upon failure the device is immediately replaced, what is the probability that there will be more than one failure in 3 years of operation?