Note: Please see attachment for more clarification.
1. For the fault tree given below,
a. Find the minimum cut sets
b. If the probability of each basic event is 0.10, what is the approximate top event probability? Using the minimum cut sets, what is the exact top event probability?
c. Find a set of mutually exclusive cut sets (using a BDD) and use those to calculate the exact top event probability.
2. If an accident requires occurrence of event I followed by event B or C so that a major consequence occurs:
a. Develop an event tree to depict all scenarios that are possible. Assume event B is triggered first.
b. If the frequency of event I is 0.1 per year and B and C may be obtained from the following fault tree, with probabilities assigned to each basic event, determine the frequency of each scenario.
c. If the consequence of each accident scenario is 100 injuries, what is the total risk of the accident?
3. Calculate the exact probability of
Assume that A, B, and C are independent, but not mutually exclusive. P(A) = 0.4,
P(B) = 0.25, P(C) = 0.8
Hello please find attached. Note I haven't had time to check my work as yet
For the fault tree given below
Find the minimum cut sets
The system will fail if any of the following scenarios occur
A and C fail (A∩C)=A.C
B and C fail (B∩C)=B.C
A and X fail (A∩X)=A.X
B and X fail(B∩X)=B.X
X will fail if either just B fails and D fails at the same time or E (on its own) fails whilst simultaneously A or B fails
Thus MCS are therefore from inspection
If the probability of each basic event is 0.10, what is the approximate top event probability? Using the minimum cut sets, what is the exact top event probability?
Approximate top event probability
To approximate the system probability we will consider the probability of an OR
function follows mutually exclusive axiom (it is only an estimation after all) that
Probability of an AND function follows
Probability of Switch event is
Probability of Emergency valve failure event is
Probability of secondary event X is thus
P(X)= P(Switch). P(EV)=0.2×0.2=0.04
Probability of Backup event is
Probability of Main event is
Finally probability of the top even failure is
P(Tank Rupture)= P(Main). P(BU)=0.2×0.14≃0.028
Exact top event probability using MCS (considering non mutual exclusivity)
Since considering the events are non-mutually exclusive we apply the probability axiom
for added probabilities
Find a set of mutually exclusive cut sets (using a ...
Fault and Event tree analysis including elements using minimum cut sets to determine top event probability of occurrence. Binary Decision is also used to derive the minimum cut sets defining a Fault Tree