At an airport, there are a number of barriers in place to prevent an aircraft from entering a runway while there is another aircraft about to take off or land. For a collision between two aircraft to happen, all the following barriers must fail: First the pilot should stop at a designated place and wait for clearance to enter the runway.This is marked by signs and flashing lights. (STOP RWY) If the air traffic controller detects the aircraft crossing the line, she will contact the aircraft and try to stop it from proceeding. (ATCWARNS) If the pilot crosses this line, the air traffic controller receives an alarm. For various reasons, these alarms may sometimes be turned off. (ALARM) The air traffic controller shall also monitor the traffic and may detect an aircraft entering the runway even if no alarm is sounded. (ATC DETECTS) If all this fails, the aircraft will enter the runway. However, an accident need not occur since this will depend on whether there is another aircraft about to take off or land. In quiet periods, this is not necessarily the case. (NO TRAFFIC)

a)      Construct an event tree with “Aircraft about to enter runway” as the hazardous event and with “Accident” or “No accident” as the end events in the event tree.

b)      The following probabilities apply: Pr(STOP RWY) = 0.995 Pr(ATC WARNS) = 0.90 Pr(ALARM) = 0.90 Pr(ATC DETECTS) = 0.80 Pr(NO TRAFFIC) = 0.70 Calculate the probability of “Accident,” given that an aircraft is about to enter the runway.

c)       c) Assume that 10 000 aircrafts enter the runway each year. Calculate the frequency of “Accident” per year. If the traffic is very dense, Pr(NO TRAFFIC) decreases to 0.30. In such a situation, the work load on the air traffic controllers also increases, and the probability that the aircraft is detected and that warning is given in time decreases: Pr(ATC WARNS | heavy traffic) = 0.6 Pr(ATC DETECTS | heavy traffic) = 0.4