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time distributions for controller intervention and self-correction. The result for controller
intervention to correct the blunderer is shown in Figure 6-2, where both the probability
density and cumulative probability distribution functions are displayed. In this example,
the minimum possible reaction time is 26 seconds, and there is about a 10 percent chance
that the correction won’t happen at all (possibly due to controller not observing the threat,
blocked radio frequency, non-responding flight crew, etc.)
BLUNDERER CONTROLLER ASSISTED RESPONSE
TIME
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
26
36
46
56
66
76
86
96
106
116
126
136
146
156
166
176
186
196
TIME (SEC)
PROB
CUM
Figure 6-2. Example of an ABRM Response Time Distribution (Hypothetical Data)
The results obtained are:
Horizontal separation requirement (R) = 116.5 feet
Vertical separation requirement (Y) = 35 feet
Vertical path separation at crossing point (H) = 38 feet
Time until crossing (Tc) = 42 seconds
Probabilities:
Blind flying collision (Pn) = 1.0 x 10-4
No blunderer correction (Pb) = 0.71
No evader correction (Pe) = 0.61
SEPARATION SAFETY MODELING
6-6
No self-correction (Ps) = 0.818
Probability of collision given a blunder (Pc) = 3.6 x 10-5
A sensitivity analysis was performed by rerunning the problem with initial path separations
of 3.6 to 4.5 nm. No other input data were changed. The ABRM has the capability to do
these analyses automatically. The results obtained are shown in Figure 6-3. Only two
values of INSEPH ( 4.0 and 4.1) were found that had a non-zero collision risk.
INITIAL HORIZONTAL SEPARATION SENSITIVITY
0.00E+00
5.00E-06
1.00E-05
1.50E-05
2.00E-05
2.50E-05
3.00E-05
3.50E-05
4.00E-05
4.50E-05
3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5
HORIZONTAL SEPARATION (NM)
P(COLLN)
Figure 6-3
Collision Risk as a Function of Initial Horizontal Separation in The Hypothetical Example
In this example the blunderer is descending at a 4 degree angle. Increasing or decreasing
the initial separation can result in the blunderer crossing safely above or below the
evader’s path. As a further extension of the sensitivity analysis, both the horizontal and
vertical blunder angles were varied independently, as shown in Figure 6-4. The vertical
angle is varied in 1 degree steps and the horizontal angle is varied in 5 degree steps. Only
one point (PHI = 120 and ALPHA1 = -4) was found that had a non-zero collision risk.
These 35 combinations were run on a 486 personal computer in under one minute.
EXISTING MODELS AND MODELING TOOLS
6-7
-6
-5
-4
-3
115
125
0.00E+00 135
1.00E-05
2.00E-05
3.00E-05
4.00E-05
P(COLLN)
BLUNDER ANGLE ANALYSIS
horizontal
angle
(degrees)
vertical angle
(degrees)
Figure 6-4
Collision Risk as a Function of Horizontal and Vertical Blunder Angles
The reader is reminded that this is only a hypothetical example, to illustrate use of the
model. In order to determine the impact of a change in separation minima and/or new
technology, the same scenario could be run under current conditions and modified
conditions. Reduced separation requirements could impact the initial separation, increase
the effective aircraft density, and reduce the self correction time (measured from the
moment the blunder occurs). The result of these considerations could either increase or
decrease the relative risk of collision, depending on the particular scenario. This example
illustrates the power of the ABRM to analyze a risk scenario and determine the relative
contributions of various factors to the overall risk.
Data Requirements
Actual data on blunder scenarios can be obtained through analysis of reports of
operational errors (OEs) and pilot deviations (PDs). OEs are cases where required
minimum separation was lost as a result of a failure of the air traffic control (humantechnical)
system. PDs are situations where separation was lost due to pilot error. Both
would provide examples and estimates of the relative likelihoods of various situations
where a potential risk of collision was observed and controller intervention was required,
often delayed, and sometimes not provided in time.
Some data on human reaction (response) times may be obtainable through analysis of
operational error and pilot deviation reports, but high-cost human-in-the-loop experiments
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a concept paper for separation safety modeling(39)
