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distributions using statistical methods. The empirical data sets generated by the real-time
simulation are not from Normal or other standard distributions, so special techniques are
required to fit curves to the data.
5.4.4 Evaluation of Simulation Results
The evaluation of the simulation results is just as important as the simulation itself. The
evaluation method should be developed as an integral part of the simulation. The data
output of the simulation should be designed specifically for the evaluation which will be
employed. The acceptance criteria should be defined before the simulation begins. For
example, in the MPAP the evaluation of the operation depends primarily on the TCV. The
TCV represents the possible collision of two aircraft. It is necessary to estimate the
probability of a TCV and then to determine an acceptable upper limit for that probability.
For example, several events must occur simultaneously for a collision to occur during
simultaneous instrument approaches. Clearly, a blunder must occur, or there would be no
significant deviation from course. Previous testing has shown that blunders less than
Worst Case (a blunder with a 30o heading change) are of negligible risk, so the blunder
must be a Worst Case Blunder (WCB). Also, the blundering aircraft must have a critical
alignment with an aircraft on an adjacent course, that is, it must be at-risk. If all of the
above events develop, a TCV will occur if the air traffic controller and the pilots cannot
react in sufficient time to separate the blundering and the evading aircraft. Since the
preponderance of fatal accidents involve only one aircraft, accident rates are based on
single aircraft accidents. Therefore, for comparison purposes, since one collision will
involve two aircraft it will be considered to produce two accidents. Assuming that a TCV
SEPARATION SAFETY MODELING
5-26
will result in a collision, the probability of a collision accident can be expressed in
mathematical terms by:
(1) P(Accident) = P(TCV and At-risk and WCB and Blunder) x 2
or
(2) P(Accident) = P(TCV|At-risk and WCB and Blunder)
x P(At-risk|WCB and Blunder)
x P(WCB|Blunder)
x P(Blunder) x 2 ,
where:
P(TCV and At-risk and WCB and Blunder) is the probability of all relevant events
occurring simultaneously, that is, an at-risk WCB that results in a TCV.
P(TCV|At-risk and WCB and Blunder) is the probability that a TCV occurs given
that an at-risk WCB has occurred. This quantity is estimated by the simulation of
at-risk WCB in the real-time and Monte Carlo simulations (i.e., the TCV rate in
the simulation).
P(At-risk|WCB and Blunder) is the probability that a WCB has critical alignment
with an aircraft on an adjacent approach.
P(WCB|Blunder) is the probability that a blunder is a WCB.
P(Blunder) is the probability that a blunder occurs during a simultaneous
instrument approach.
The factor of 2 represents two accidents per collision.
Ideally, the probability of an accident occurring during the tested approach operation
could be computed from Equation (2) and a determination made of its acceptability. An
acceptability criterion can be based on a Target Level of Safety.
5.4.5 Obtaining a Maximum Allowable TCV Rate Based on a Target Level of
Safety
Determining a Target Level of Safety
An example of the determination of a Target Level of Safety (TLS) is a method applicable
to parallel approach operations. This method can adapted to en route operations.
The total number of air carrier accidents, as well as the number of fatal accidents on final
approach, has been extracted from National Transportation Safety Board (NTSB) data for
APPROACHES TO COLLISION RISK ANALYSIS
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the time period, 1983-1989. This number, together with the total number of ILS
approaches flown during this time period, leads to an estimated fatal accident rate of 4 x
10-7 fatal accidents (ACC) per ILS approach (APP) during IMC. There are a number of
causes of accidents during final approach, such as structural failure, engine failure, or
midair collision. An initial estimate is that there are nine possible causes of accidents on
final approach. A tenth possible accident cause, a collision with an aircraft on an adjacent
approach, is created with the implementation of simultaneous parallel approaches.
For simplicity of model development, it is assumed that the risks of the ten potential
accident causes are equal. Thus, the contribution of any one of the accident causes would
be one-tenth of the total accident rate. Based on this, the target safety level for midair
collisions on simultaneous parallel approaches is 4 x 10-8, or
1 ACC
25 mill APP
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a concept paper for separation safety modeling(34)
