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initial failure event is a “blunder” where one aircraft (Blunder Aircraft) deviates from its
approach centerline and crosses a “No Transgression Zone” (NTZ), creating a potentially
hazardous condition, namely, a potential collision with the other aircraft (Evader Aircraft).
The total lateral separation collision risk (top event of fault tree) is thereby modeled as a
hierarchical fault tree structure depicting the various human, equipment, and ATC
procedural failures that contribute to the overall collision risk and their respective
estimated probability distributions and/or values. Similarly, for the In-Trail collision risk
fault tree, the two contributing conditions or scenarios, Simultaneous Runway Occupancy
and Wake Vortex Encounter, are modeled as fault trees with operational data acquired
from FAA and ICAO.
Although no specific collision risk analysis for en route or terminal airspace has been
identified for applying the Event-Sequence Analysis (ESA) methodology to ATC collision
risk modeling, other flight operations have been modeled using ESA. For example, an
ESA was conducted for determining the risk of a catastrophic accident of a single aircraft
during takeoff by delineating the particular series of events which would cause a
hazardous takeoff procedure and subsequent accident. This particular ESA, for example,
is comprised of a sequence of key events and conditions such as: “First Officer fails to set
Flap Lever down during taxi-out,” or “Speedbrake/Flap Warning Test is missed during
taxi-out,” among others, which potentially contribute to an accident during takeoff where
the flight crew had failed to move the Flap Handle down prior to takeoff. A similar study
focused on the sequence of events which lead to an invalid setting of the engine thrust
setting indicator.
5.3 PROBABILISTIC, ANALYTIC MODELS
5.3.1 Probabilistic/Analytic vs. Numerical Simulation Models
The terms “probabilistic model” or “analytic model” are used in this discussion to refer to
models that do not employ time-step or event-step numerical simulation (usually with
Monte Carlo techniques), but rather use “closed-form” mathematical equations. This
discussion concentrates on models of midair collisions applicable to airspace where radar
separation is provided, and the question of how reducing horizontal separation minima
would affect collision risk.
SEPARATION SAFETY MODELING
5-8
Some of the advantages of probabilistic models are:
1. Computational efficiency - Numerical simulation models often expend computational
effort to produce intermediate values of no interest, e.g., moving aircraft step-by-step
through the airspace and computing the distance to all other aircraft at each step.
Analytic models tend to get right to the point, making them much more efficient. For
many applications this is no longer the advantage that it used to be now that vast
computing power is available on almost everyone’s desk. However, midair collisions
are such rare events that, unless the problem is cleverly decomposed, the number of
simulation iterations needed to obtain meaningful results will be enormous.
2. Consistency - Analytic models produce the same answer every time that they are run
with the same input data. Monte Carlo (simulation) models will produce different
results each time, as a different set of random numbers are drawn. Thus, they must be
exercised many times to obtain sufficient statistics. Tests have been developed to
determine how many replications are required to assure sufficiently accurate results,
but these usually require either an unverifiable assumption about the distribution of the
desired statistic or a huge number of replications (based on non-parametric statistics).
3. Clarity - Analytic models generally have fewer logical quirks hidden deep in the
computer code that may, under special circumstances, cause unrealistic intermediate
results that go undetected. The equations in an analytic model are usually made
available for the user to see. This doesn’t mean, however, that the equations cannot be
faulty or that the software coding of the equations erroneous.
4. Development time - Monte Carlo models are often very complex and costly to
program, but probabilistic models can require time-consuming mathematical
derivations.
5. Accuracy - When the ‘desired’ outcome is a very unlikely event (e.g., a midair
collision), either a huge number of Monte Carlo trials would be required, or the
simulation would require an assumed set of conditions that make the event relatively
likely. One must then temper the computed probability with an estimate of the
　
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