Question

An engineer is asked to estimate the probability that a hospital will be completely without power during a given period of time. The hospital typically gets its power from the power grid. For the purpose of this problem, assume that power outages causing loss of grid power can be caused by severe weather (probability = 1*10^-2), equipment failure (probability = 5*10^-3), or power demand exceeding supply (probability = 1*10^-3). The hospital also has two backup generators that automatically start when there is a loss of grid power. Each generator can provide enough power for the hospital on its own. Each generator has a probability of not starting of 1*10^-2.

a) Construct a fault tree to represent the hospital being without power based on the assumptions described above.

b) What is the probability that neither generator starts?

c) What is the probability of the hospital being completely without power?

Answer 1

(a) Here is the fault tree to represent the hospital being without power based on the assumptions described above :

(b) P(neither generator starts) = P(1st generator not startng) + P(2nd generator not startng)

P(neither generator starts) = (1/100)*(1/100)

P(neither generator starts) = 1/10000

(c) P(hospital being completely without power) = P(Severe weather and both generator not startng) + P(Equipment failure and both generator not startng) + P(power demand exceeding supply and both generator not startng)

P(hospital being completely without power) = ((1/100)*(1/10000)) + ((5/1000)*(1/10000)) + ((1/1000)*(1/10000))

P(hospital being completely without power) = 1.6*(10^(-6))