MEM 361 Engineering Reliability
Problem Set 5
1) Suppose that a fault tree has three minimal cut sets with probabilities ,
, . Find an upper bound for the probability of the top event.
123
,,CCC
()
10.03PC =
()
20.12PC =
()
30.005PC =
2) The system shown below is designed to deliver emergency cooling to a nuclear reactor:
In the event of an accident, the protection system sends a signal to the two pumps and
four valves. The valves open, the pumps start and coolant is supplied to the reactor.
The following failure probabilities are associated with the basic failure events:
The probability that the protection system will not deliver a signal to the pump and
valve actuators
5
10
ps
p−
=
The probability that a pump will fails to start when the actuation signal is received 2
210
p
p−
=×
The probability that a valve will fails to open when the actuation signal is received 1
10
v
p−
=
The probability that the reservoir will be empty when the accident occurs 5
0.5 10
r
p−
=×
a. Draw a fault tree for the failure of the system to deliver any coolant,
b. Evaluate the probability that such a failure will occur.
c. Draw the reliability block diagram.
d. Evaluate the reliability of the system
3) A system consists of two components in series. The component rel1abilities are and
. It is decided to add two redundant components. Which of the following is most
effective in improving system reliability:
10.98R=
20.94R=
a. Duplicate the system in high level redundancy,
b. Duplicate the system in low level redundancy,
c. Replace the second component with 1-out-of-3 redundancy.