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aircraft controls, and
c. The first aircraft responds to the controls in time to avoid the collision;
and/or
d. The controller orders the second aircraft to maneuver, and
e. The pilot of the second aircraft interprets the controller’s command and moves the
aircraft controls, and
f. The second aircraft responds to the controls in time to avoid the collision;
SEPARATION SAFETY MODELING
5-16
or
2. The pilot of the first aircraft detects the threat prior to ATC notification, and
a. The pilot of the first aircraft moves the aircraft controls, and
b. The first aircraft responds to the controls in time to avoid the collision;
or
3. The pilot of the second aircraft detects the threat prior to ATC notification, and
a. The pilot of the second aircraft moves the aircraft controls, and
b. The second aircraft responds to the controls in time to prevent the collision;
or
4. The aircraft collide.
The above logic does not include every possible combination of events and ignores the
relatively remote possibility that both aircraft execute avoidance maneuvers which result in
a collision. Note that the question is not whether or not an avoidance maneuver is
executed, but whether it is executed in time. This time is the sum of times required for
each event in one or another of the processes. If a process is not executed at all, this can
be represented by the time being excessive.
The times required for events 1c and 2b are the same, and the times required for events 1f
and 3b are the same. But the times for events 1c and 1f could be different if, for example,
the aircraft are of different types. The times required for events 1b and 1e could be
different, if, for example, the pilots’ skills and/or the types of aircraft are different.
The time required for a particular event could be represented by a discrete distribution
(perhaps obtained through experiments) in seconds from some given starting point. Event
1a might be measured from the time that the aircraft begin heading on a collision course,
perhaps due to a blunder or belated detection of a pending conflict. It includes the time
required to decide on an avoidance strategy and to establish communication with the
aircraft. It depends on the number of aircraft being controlled, and other controller
workload factors. Events 1b and 1d should be measured from the time that event 1a is
completed (the controller completes communication with the first aircraft). The time
required for event 1c should be measured from the time that event 1b is completed, etc.
The distribution of the total time required to complete a series of events, each of which
begins when the previous event ends, can be obtained by a series of convolutions of the
(assumed to be independent) distributions. These series of event time convolutions are
computed, for example, in the Analytic Blunder Risk Model (ABRM) [see Chapter 6].
APPROACHES TO COLLISION RISK ANALYSIS
5-17
5.3.5 Analysis of Separation Standards
Following the above discussion on intervention considerations, the probability of a
collision can be approximated by:
Pc = Pcc x Pbf x (1-P1)x(1-P2)
where:
Pcc is the probability that two aircraft are on conflicting, crossing courses, and
Pbf is the probability that two aircraft that are on conflicting, crossing courses will arrive at
the crossing point close enough in time to result in a collision, assuming that no
intervention occurs.
P1 is the probability that aircraft 1 modifies its course in time to avoid a collision, and
P2 is the probability that aircraft 2 modifies its course in time to avoid a collision.
P1 = Pp1 + Pa1 - (Pa1 x Pp1), where
Pp1 is the probability of pilot detection and intervention in time, and
Pa1 is the probability of ATC-induced intervention in time, etc.
Suppose that two aircraft are separated by exactly the required amount when a blunder
occurs. A reduction in separation criteria can affect the individual probabilities resulting
from a blunder, as follows:
1. Pcc could be increased or decreased, as a blunder in a particular direction (in the
horizontal plane, the vertical plane, or both) would be more or less likely to put the
aircraft on conflicting courses.
2. Pbf could be increased, as the aircraft might be more likely to arrive at the conflict point
at the same time.
3. P1 and/or P2 could be reduced, as there would be less time for the pilots and controller
(it is assumed that both aircraft would be controlled by the same sector) to intervene.
There would also theoretically be less time for airframe reaction and a more severe
avoidance maneuver might be required.
One computer model for making these computations is the Analytical Blunder Risk
　
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