Question

A small city is situated on the countryside. Upstream form the city is a dam that provides the city's water supply. If the dam was overtopped by water, then the dam would fail and all of the water would flood through the city. There is also a danger that the dam might collapse when it is full of water and cause it to fail, also flooding the city.

A) Draw a fault tree for the head event “Dam fails and floods the town” using the following basic events The possibility of dam collapse is (P=0.01)

There is a weakness in the dam that would allow collapse to cause the dam to fail (P=0.1).

Storm occurs that overtops the dam provided that it is mostly full (P=0.002)

Storm occurs that will overtop the dam no matter how full the dam is (P=0.0004)

Dam is mostly full (P=0.4).

B) Determine the probability that the dam will fail and flood the town. For the hours of daylight (assume 12 hours on average) there is someone working at the dam who could send a warning to the city if the dam failed.

There is an 80% probability that this person would be able to get the message to the city in time to evacuate. If the dam failed during the night no one would see it, but there is a 60% chance that the weather conditions would be such that the noise of the dam breaking could be heard by someone in the city and give them enough warning to evacuate everybody.

However, every Saturday night the city has a large party, and nobody would be able to hear if the dam failed anyway.

C) Draw an event tree that can be used to determine the conditional probability that the city will receive warning in time to evacuate.

D) Determine this conditional probability of receiving the warning on time.

E) What is the overall probability that the town will be flooded without an evacuation occurring? Hint: consider your answer for (b).

Answer 1

Since there are some diagrams, I preferred a handwritten note. Results are tabulated in the answer for your easier understanding. Hope that it is clear for you and it really helped you.

In case of any doubt, please feel free to ask in the comment section. Thank you.