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P(Sx) = ò f (x) f (x + Sx)dx (3)
where,
P(Sx) = probability of overlap given Sx
6.6 PARALLEL APPROACH BLUNDER MODELING
Here, as in the oceanic lateral modeling, a blunder refers to an aircraft that strays from its
own path into the path of other aircraft. In evaluating the safety of parallel approach
operations, the FAA has analyzed the consequences of a particular, worst-case blunder as
an indicator of the relative safety of changes in ATC procedures and runway separation
distances. Although this specific blunder scenario is referred to in a number of studies, the
terms of reference are inconsistent. Within this discussion, it will be referred to as the
Parallel Blunder Scenario.
Real-time Simulations at the FAA William J. Hughes Technical Center (FAATC)
The Parallel Blunder Scenario requires a controller to detect when the blundering aircraft
leaves the Normal Operating Zone (NOZ) and to communicate break-out instructions to
any aircraft that would be threatened by the blunder, and requires the threatened aircraft to
execute the break-out maneuver. Real-time simulations at the FAATC include human
interaction with trained personnel in the roles of controllers and pilots. Smaller, faster
EXISTING MODELS AND MODELING TOOLS
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computer models have been a useful complement to the extensive simulations at the
FAATC.
The Blunder Risk Model (BRM)
The BRM was developed by Lincoln Laboratory as part of the FAA’s demonstration
project for the Precision Runway Monitor (PRM). The intent of the PRM program was to
develop equipment, algorithms, and procedures that would allow safe operation of
independent approaches to parallel runways separated by as little as 3000 feet.
Purpose and application
The BRM executes the Parallel Blunder Scenario as a Monte Carlo simulation.3 Because
it is a computer model, the BRM can execute experiments more quickly and easily than is
possible with the real-time simulations at the FAATC. The BRM incorporates the
definitions of events and operational requirements used in the Parallel Approach Scenario
at the FAATC.
Main approach
The Parallel Blunder Scenario analyzes the situation only after a blunder has been
committed. The BRM incorporates the PRM alert logic as a part of the simulation,
introducing a source of random variation in the alert warnings that are available to the
controllers. Human interaction times and delay distributions are required inputs to the
BRM; the computer model cannot produce new information about the response times of
controllers or pilots. The Monte Carlo logic used in the BRM samples one source of
delay after another, in sequence, until the evader maneuver begins, or until the blundering
aircraft is safely past the evader.
Main inputs and outputs
For each encounter between a blundering aircraft and an evader, the primary output is the
distance between the two aircraft at the point of closest approach. The encounter
geometry is based on a uniform longitudinal distribution of evader traffic and a lateral
distribution based on measurement of aircraft performance at operational airports. Evader
maneuvers are chosen from a fixed, discrete set of maneuvers that were observed and
recorded in real-time simulations at the FAATC and elsewhere. The BRM results are
summarized as a frequency distribution of minimum separations observed in the simulated
iterations of the scenario.
3 A Monte Carlo simulation produces a probability distribution of an output measure that depends on
several statistically determined input measures. The specific approach of Monte Carlo simulation is to
randomly sample from all possible combinations of the input parameters in proportion to their probability
density functions in order to build up an approximate probability for the output measure.
SEPARATION SAFETY MODELING
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The output measure is the minimum separation between the blundering aircraft and an
aircraft using the parallel approach path. The major events in an encounter are the
blunder, the warning, the intervention, the evasion, and the termination. The minimum
separation distribution is analyzed to determine if the intervention performance is adequate
to protect the parallel approach stream from a worst-case blunder. Intervention
performance is measured by a resolution time random variable computation shown in
equation 4.
tres = talert + tcont + tcomm + tpilot (4)
where,
talert = time from the blunder to the alert or warning
tcont = time from the alert to when the controller issues an instruction
tcomm = communications delay in message transmission
tpilot = time from ATC message receipt until the aircraft starts to turn
　
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