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Ideally, normalization procedures should consider the dis- The illustration for overrun incidents shows a typical prob-
tance required relative to the runway distance available dur- ability distribution for the stopping location during a landing
ing the operation. However, the attempt to incorporate this or rejected takeoff operation. (The illustration is not to scale
factor proved difficult due to a lack of available information and is only intended to help understanding the concept.) The
to compute the distances required, for both the accident data great majority of aircraft will stop within the runway bound-
and NOD. aries, represented by the lightly shaded area of the probabil-
In addition, some factors cannot be normalized, such as ity distribution. However, in a few cases, the aircraft may not
the pilot's skill or differences in safety records between coun- be able to stop before the runway end and will stop on the
tries. Despite these difficulties the technique utilized in this RSA or even beyond. This probability of overrunning
study creates a larger pool of relevant and comparable data the runway is represented by the dark shaded area. It would
for sound model building. Results from models built with be best to model the whole probability distribution for the
normalized accident and normal operations data then can be aircraft stopping location, but this information is not avail-
applied to specific airports through denormalization. able for NOD, and an alternative modeling approach was re-
quired in a two-step process: evaluating the probability an
aircraft will in fact overrun the runway, and modeling the
Development of Risk Models
likelihood the aircraft will stop beyond any given distance
In this study overrun and undershoot risk models were de- from the runway threshold.
veloped to allow the analysis of RSAs in the light of specific The same concept was used for the point of first impact
factors related to existing operation conditions. The basic (POFI) during landing undershoots. Figure 4 depicts the
concept was to model the probability distribution for wreck- probability distribution for the touchdown location. Again,
age location in the proximity of the runway threshold. The for the great majority of operations, the aircraft will touch-
concept is illustrated in Figure 3 for overruns and in Figure 4 down within the runway boundaries, represented by the
for undershoots. lightly shaded area of the probability distribution. The dark
m
P {Location > x} = eax
Stop Location
Probability Distribution
RSA
x
y
Figure 3. General concept for modeling aircraft overruns.
m
P {Location > x } = eax
Touchdown Location
Probability Distribution
RSA
x
y
Figure 4. General concept for modeling aircraft undershoots.

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n
P {Location > y } = eb x
y
Figure 5. General concept for modeling aircraft lateral deviation.
shaded area represents the probability the aircraft will land ments carried out at reference airports and the number of acci-
before the approach end of the runway. dents that occurred during those movements. Loughborough
In addition, it was necessary to model the probability University has pioneered the use of NOD to include a multitude
distribution for the aircraft wreckage location relative to the of risk factors in the assessment of accident probability. Using
extended runway centerline. The concept is represented in this approach allowed a far more discriminating analysis than
Figure 5. Using the "x" and "y" models combined will allow relying solely on the accident rate. As a result, conclusions on
users to evaluate RSA off standard dimensions and overall RSA risks will reflect better the actual conditions and circum-
configuration. The distribution only represents the location stances of specific airports.
distribution for aircrafts overrunning or undershooting the
runway. Accident Location. In reality, the probability of an acci-
An initial analysis of the database and NOD was required to dent is not equal for all locations around the airport. The
determine which risk factors were available to be built into the probability of an accident in the proximity of the runways is
parametric models. The generic model and the wider insight higher than at larger distances from the runway. This de-
gained from the database allowed an initial generic estimate of pendence is represented by the accident location model,
risk for a given situation to be made and identification of which is the second main element of the current methodol-
whether there were other significant risk factors that applied. ogy. The accident location model is based on historical data.
The three-part modeling approach was built for each accident The distribution of accident locations relative to the runway
type, as represented in Figure 6. Before developing the final will be modeled through statistical functions introduced by
model structure, the available data were evaluated statistically, Eddowes et al. (2001). By combining the accident location
in order to develop the proper model structure and to ensure model with the accident probability, the local probability of
the parameters were compatible with model assumptions. an accident can be calculated for each runway end.
Accident Consequences. The consequences of an acci-
Approach Elements
dent are a function of the dimensions of the actual RSA, of the
Event Probability. The likelihood of an aircraft overrun aircraft and impact parameters (such as aircraft size, quantity
or undershoot accident or incident depends on the operation of on-board fuel, impact angle, etc.), and of the local type of
conditions, including airport characteristics, weather condi- terrain and obstacles. The size of the accident area is not equal
tions, and aircraft performance. for every airport or area within the airport. The influence of
The probability of an accident per movement--the accident the aircraft and impact parameters and the type of terrain on
rate--is determined from historical data on numbers of move- the size of the consequence area, as well as the lethality and
Three-Part Risk Model
Event Location Accident
Risk
probability probability consequences
Location
probability,
Operating Operating
obstacle location,
conditions conditions, terrain size and type,
aircraft type
Figure 6. Modeling approach.

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damage of the consequences, are defined in the consequences adds to the understanding of cause-result relationships of the
model, the third main element in the current methodology. two accident types. This constitutes a causal element in the
For this purpose, lethality is defined as the actual probability risk models, so the modeling tool developed can be used to
of being killed within the consequence area. Aircraft damage assess risk reduction strategies and estimate future risk levels,
is translated as the direct cost of property loss for an accident. given trends in influential factors in an airport context.
A previous Loughborough University study on overruns
found that the model developed for landing overrun risk using
Accident/Incident Probability Model NOD on excess landing distance available is 22 times more
predictive than models based on flight type alone (Kirkland,
To examine the accident propensity associated with differ-
2001). Additional analyses using NOD have been conducted
ent factors (e.g., environmental conditions), logistic regression
since, and they continue to show the importance of assessing
was used to develop statistical models for accident/incident
the criticality of risk factors beyond the simple accident/
occurrence probability.
movement rate (Wong et al., 2005b, 2006).
A number of numerical techniques could be used to carry out
the multivariate analysis, but logistic regression was preferred.
First, the technique is suited to models with a dichotomous out- Accident/Incident Location Model
come (incident and nonincident) with multiple predictor vari- The model structure selected for accident location was
ables that include a mixture of continuous and categorical pa- used by Eddowes et al. (2001) and is in the following form:
rameters. Logistic regression also is appropriate for case-control
studies because it allows the use of samples with different sam- P{Location > x} = e - axn (2)
pling fractions, depending on the outcome variable without giv-
where
ing biased results. In this study, logistic regression allowed the
sampling fractions of accident flights and of normal flights to be P{Location > distance} = the probability the overrun/
different. This property is not shared by most other types of re- undershoot distance along the
gression analysis (Nagelkerke et al., 2005). runway centerline beyond the
Backward stepwise logistic regression was used to calibrate threshold is greater than x;
the three frequency models because of the predictive nature x = a given location or distance be-
of the research. This technique is able to identify relationships yond the threshold; and
missed by forward stepwise logistic regression (Hosmer and a, n = regression coefficients.
Lemeshow, 2000; Menard, 2001). Due to the more stringent
data requirements of multivariate regression, cases with miss- This dependence is represented by the accident location
ing data were replaced by their respective series means. model, which is the second main element of the current
To avoid the negative effects of multi colinearity on the methodology. The accident location model is based on his-
model, correlations between independent variables were torical data on accident locations. The distribution of acci-
tested first to eliminate highly correlated variables, particu- dent locations relative to the runway was modeled through
larly if they do not significantly contribute to explaining the statistical functions. By combining the accident location
variation of the probability of an accident. model with accident probability, the local probability of an
The basic model structure selected for this study is in the accident can be calculated for each runway end.
following form: When plotting the percentage of accidents where the air-
craft stopped beyond a certain distance from the threshold,
1 in case of overruns, or first impacted the terrain, for under-
P{ Accident _ Occurence} = (1)
1+ e b0 +b1X1 +b2 X 2 +b3 X 3 +... shoots, the probability diminishes the greater the distance is,
as depicted in Figure 7.
where
The probability and location models will provide a quantita-
P{Accident_Occurrence} = the probability (0-100%) of an tive assessment based on operating conditions for a specific
accident type occurring given airplane landing or taking off at a specific runway. In addition,
certain operational conditions; it is necessary to relate these probabilities with the RSA condi-
Xi = independent variables (e.g., tions to provide an assessment of the probability that the con-
ceiling, visibility, crosswind, sequences of an incident are severe. This is the final component
precipitation, aircraft type); and of the approach, described in the following section.
bi = regression coefficients.
Consequence Model
The use of NOD in the accident frequency model provided
a major improvement in the modeling of accident occur- The consequences modeling approach should provide a
rence, as discussed previously. The analysis with NOD also qualitative assessment of the severity of an accident, based on

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100% The speed necessary to cause significant damage to the air-
craft and potentially severe consequences should be judged
80% based on the type of aircraft, type of terrain, and type of obsta-
Prob{distance > x }
cle. For this study, only general recommendations are provided
60% to assess the interaction between the aircraft and obstacles.
Using some simple assumptions it is possible to evaluate the
40% overall risk of severe consequence accidents.
One of the difficulties posed to evaluate consequences of
20% accidents was to integrate the number and severity of injuries
with the property loss. It was not possible or practical to eval-
0%
0 500 1000 1500 2000
uate indirect consequences such as lost revenue, lost work
Distance x from Threshold (ft) time, disruption of flight schedule, and negative customer re-
action to accidents.
Figure 7. Typical trend for wreckage location
In this study, estimates for direct costs of accidents are pro-
model.
vided as a means to integrate personal injury and property
loss. Although it is estimated that indirect costs typically rep-
the location model and the existing runway characteristics, to resent four times the value of direct costs, only the latter will
include dimensions of existing RSA, airplane weight, location be used in this study. The parameters that were evaluated
and type of obstacles, and topography of surrounding terrain. include the cost of the accidents, and number and type of
The approach used in this project was to model the probability injuries. The relationships between these consequence
of severe consequences using the frequency and location mod- parameters and potential independent variables include
els, coupled with existing RSA configuration and obstacles. the wreckage path length, the number of obstacles hit during
The consequences of an accident depend on several factors the accident, the location of these obstacles, and land use type
that are difficult to model, such as the energy of the crash for the area beyond the existing RSA.
(speed, aircraft weight, and size), quantity of fuel and occur-
rence of fire after impact, type of obstacle (height, depth, ma-
terial, size), impact angle, and the local type of terrain. Initial Accident Costs
attempts to model consequences focused on the relationship The consequences of accidents, as documented in investi-
between the raw or normalized distances and the severity of gation reports, are described in terms of the number of
the accident, reflected by the amount of damage and cost of injuries and the level of damage to the aircraft. Although
injuries. The overall consequences of the accidents were quan- third-party injuries also were accounted for in this study,
tified by the total direct costs for injuries and aircraft damage. property loss not related to aircraft damage was not evaluated
The approach proved difficult to implement because the re- for the lack of information. Injuries are classified according
lationship between accident location and consequences was to ICAO criteria into four groups: none, minor, serious and
poor. In many situations the consequences were related to the fatal. The number of passengers and crew members for each
speed that the aircraft hit an obstacle and the type of the obsta- level generally is available in the accident reports. Based on
cle. Information for the former was not available for the great the total number of passengers/crew on board the fatality rate
majority of cases. Therefore, the efforts to model consequences for each accident was calculated. Damage to aircraft also is
were directed to providing a rational approach that incorpo- described according to four classification groups: none,
rated the location model. The basic idea is simple but effective. minor, substantial, and destroyed.
The higher the speed, and hence the energy when an aircraft In addition to the raw classification, direct cost of acci-
hits an obstacle, the greater the consequences. The sturdier the dents was calculated based on the number and type of
obstacle, the greater the consequences. The larger the obstacle, injuries, as well as the damage to the aircraft. The basic
the greater the probability the aircraft will hit the obstacle. source for accident cost is the Guide for Economic Values for
The speed of the aircraft striking the obstacle is related to FAA Investment and Regulatory Decisions (GRA, 2004). The
the distance the aircraft would take to stop if no obstacles objective of this report is to present a set of cost items and
were present in the area adjacent to the runway ends. Based quantify the specific values recommended that FAA use in
on the location model, the terrain type, and the deceleration future regulatory evaluations in the conduct of benefit-cost
model developed by Kirkland (2001), the probability the air- and other evaluations of investments, including certain
craft moving above a certain speed when hitting the obstacle Airport Improvement Program (AIP) grants, and regula-
can be estimated. tions subject to FAA decision making. They also are used by