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22
Reported Events per Year
18
16 ACC
INC
Number of Occurrences
14
12
10
8
6
4
2
0
78
80
82
84
86
88
90
92
94
96
8
00
02
04
06
9
19
19
19
19
19
19
19
19
19
19
19
20
20
20
20
Year
Figure 10. Events per year.
a much higher number of incidents compared to accidents. sis method proposed to a data set of incidents and accidents
One possible explanation for this phenomenon would be that combined.
some incidents are unreported. Therefore, an analysis of the Another factor that might distort the form of the curve is
number of unreported incidents was carried out. the obstacle environment beyond the runway end. An obsta-
The methodology for evaluation of under reporting inci- cle might cause the aircraft to come to a stop earlier than it
dents is based on the assumption that there is a progressive might otherwise. Generally, there is an increased probability
decrease in the probability of travel to any given distance of an aircraft encountering an obstacle the farther it has trav-
from the runway end with increasing distance. Such behavior eled, and particularly when it has traveled farther than the
is evident from the empirical accident and incident data set RSA, this effect will lead to a reduced probability of aircraft
and is consistent with theoretical considerations of the nature traveling to greater distances than would otherwise be the
of the event. The same basis considerations apply to LDOR, case. The implications of this phenomenon required further
TOOR, and LDUS. Behavior of this type can be represented consideration as part of this analysis.
by a cumulative probability distribution function of the fol- The analysis of unreported incidents is presented in Ap-
lowing form: pendix D, and the results are summarized in Table 6. Based
on these numbers, different weights for statistical modeling
PROB{d > x} = e - axn (3)
were used to reflect the expected rate of incidents relative to
where PROB{d > x} is the probability of traveling a distance accidents.
d greater than x.
Where there is full reporting of events it is expected that the
Probability of IncidentFrequency
available empirical data should fit a function consistent with
Models
this basic form. Where there is under-reporting, some dis-
tortion in the apparent behavior can be expected. Failure to The chance of an aircraft overrunning or undershooting a
report is expected to be more likely for events where the dis- runway depends on the probability of accident per aircraft
tance traveled off the runway is relatively low. The reported movement and the number of movements (landings and
cumulative probability distribution (CPD) will be depressed takeoffs) carried out per year.
at lower values of x but co-incident with the full distribution Logistic regression, discriminant analysis, and probit
at higher values, as shown schematically in Figure 17. analysis were evaluated for modeling the probability of air-
There may be other factors that distort the form of the craft overrun and undershoot events. Discriminant analysis
CPD. A data set of incidents is expected to lack a dispro- was not used because it involves numerous assumptions,
portionate number of events at greater distances, since including requirements of the independent variables to be
these would be expected to more likely result in more seri- normally distributed, linearly related, and to have equal vari-
ous consequences and be classified as accidents. On that ance within each group (Tabachnick and Fidell, 1996).
basis, it is likely to be most appropriate to apply the analy- Logistic regression was chosen over probit analysis because
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Table 4. Anomalies during aircraft overrun
and undershoot events.
Category Anomaly Type
Aircraft System Fault Tire
Hydraulic
Power
Brake
Other
Wildlife Hazards Bird strike
Other
Weather Low Visibility
Wind Shear
Tailwind
Crosswind
Gusts
Low Ceiling
Strong Winds
Turbulence
Freezing Rain
Rain
Other
Human Error Fatigue
Communication/Coordination/
Planning
Pressonitis
Visual Illusion
Other
Runway Surface Wet
Contamination / Low friction Standing Water
Rubber
Oil
Slush
Snow
Ice
Paint
Construction
Downslope
Other
Approach/Takeoff Unstabilized Approach Approach Below Flight
Procedures Path
Approach Above Flight
Path
High Speed
Low Speed
Long Touchdown
Takeoff rejected at high speed
Other
the latter does not give the equivalent of the odds ratio and relationships missed by forward stepwise logistic regression
changes in probability are harder to quantify (Pampel, 2000). (Hosmer and Lemeshow, 2000; Menard, 2001). Due to the
Logistic regression is suited to models with a dichotomous more stringent data requirements of multivariate regression,
outcome (incident and nonincident) with multiple predictor cases with missing data were replaced by their respective
variables that include a mixture of continuous and categori- series means.
cal parameters. Logistic regression also is appropriate for Every risk factor available in both Accident/Incident data-
case-control studies because it allows the use of samples with base and NOD were used to build each model. Table 7 shows
different sampling fractions depending on the outcome vari- the final parameters retained by the backward stepwise logis-
able without giving biased results. In this study, it allowed the tic regression as relevant independent variables for each of the
sampling fractions of accident flights and normal flights to be frequency models.
different. This property is not shared by most other types of It should be noted that it was not possible to include some
regression analysis (Nagelkerke et al., 2005). risk factors in the frequency models, for example, the ratio
Backward stepwise logistic regression was used to calibrate between the landing distance available and the landing
the three frequency models because of the predictive nature distance required. Although a possible important factor to
of the research. The selected technique is able to identify assess runway criticality, the lack of information for landing
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Frequency Distribution of Anomalies for Landing Overruns
70%
65%
ACC INC
60% 58%
53%
51% 52%
50%
39%
40% 38%
% ACC/INC with Anomaly
30% 28% 27%
20%
14%
10%
0% 0%
0%
Aircraft System Wildlife Hazard Weather Condition Human Error Runway Conditions Approach/Takeoff
Fault Procedures
Figure 11. Frequency of anomalies by category (LDOR).
distance required in the normal operations data precluded but, on the other hand, a larger safety factor for distances
the use of such variables in the frequency models. However required also should be expected for most flights operating
it is difficult to evaluate how much improvement such a fac- in longer runways.
tor would bring to the model accuracy. Theoretically the The goal was to develop risk models based on actual ac-
runway length always should be compatible with the dis- cidents/incidents and normal operation conditions so that
tances required by the aircraft under certain conditions. In the probability of occurrence for certain conditions may be
this sense the new factor may bring little benefit to the model estimated. The use of such models will help evaluate the
Frequency Distribution of Anomalies for Landing Undershoots
80%
ACC INC
70% 67%
65%
59%
60%
50%
44%
% ACC/INC with Anomaly
40% 38%
31%
30% 29%
24%
20%
12%
10%
2% 2%
0%
0%
Aircraft System Wildlife Hazard Weather Human Error Runway Approach/Takeoff
Fault Condition Conditions Procedures
Figure 12. Frequency of anomalies by category (LDUS).
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Frequency Distribution of Anomalies for Takeoff Overruns
80%
ACC INC
69%
70% 68%
64%
60% 56%
51%
50%
% ACC/INC with Anomaly
40% 38%
33%
30%
24%
20%
14%
11%
10%
5% 5%
0%
Aircraft System Wildlife Hazard Weather Human Error Runway Approach/Takeoff
Fault Condition Conditions Procedures
Figure 13. Frequency of anomalies by category (TOOR).
likelihood of incident occurrence for a runway that is sub- P{Accident_Occurrence} = s the probability (0-100%) of an
ject to certain environmental and traffic conditions over accident type occurring given
the year. certain operational conditions;
The frequency model is in the following form: Xi = independent variables (e.g. ceil-
ing, visibility, crosswind, tail-
1
P{ Accident _ Occurrence} = (4) wind, aircraft weight, runway
1+ e - (b0 +b1X1 +b2 X 2 +b3 X 3 +...)
condition, etc.); and
where bi = regression coefficients.
Landing Overrun - Most Significant Anomalies
70%
60%
% of Total for Event Type
50%
40%
30%
20%
10%
0%
R- AT- AT-High
SysF- SysF- W- W- Low W- W- W- H-Inc H-
R- Wet Contam Long Spd
Brake Other Rain Visib. Tailwind Xwind Gusts Plan. Other
/LF TDown App
All 12.8% 6.2% 31.5% 18.3% 17.9% 16.1% 11.4% 17.6% 20.1% 39.2% 53.5% 38.1% 25.3%
Acc 14.2% 10.8% 35.0% 21.7% 21.7% 20.8% 17.5% 26.7% 30.8% 35.8% 42.5% 45.0% 33.3%
Inc 11.8% 2.6% 28.8% 15.7% 15.0% 12.4% 6.5% 10.5% 11.8% 41.8% 62.1% 32.7% 19.0%
Anomaly
Figure 14. Most frequent anomalies (LDOR).
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Landing Undershoot - Most Significant Anomalies
50%
45%
40%
% of Total for Event Type
35%
30%
25%
20%
15%
10%
5%
0%
W- H- AT- AT-Low
W- W- Low W- W- W- Low H-Inc H- R- AT-
Wind Visual Low Spd
Rain Visib. Xwind Gusts Ceiling Plan. Other Constr. Other
Shear Illusion App. App
All 21.3% 43.6% 8.5% 9.6% 17.0% 7.4% 19.1% 16.0% 11.7% 8.5% 22.3% 11.7% 17.0%
Acc 30.6% 46.9% 10.2% 18.4% 26.5% 12.2% 19.1% 16.0% 11.7% 4.1% 22.3% 14.3% 24.5%
Inc 11.1% 40.0% 6.7% 0.0% 6.7% 2.2% 17.8% 15.6% 8.9% 13.3% 15.6% 8.9% 8.9%
Anomaly
Figure 15. Most frequent anomalies (LDUS).
Before logistic regressions were performed, it was ensured tion terms that are the cross-product of each independent
that all assumptions for the statistical procedure were met. variable times its natural logarithm [(X)ln(X)]. The logit lin-
Logistic regression is relatively free from assumptions, espe- earity assumption is violated if these terms are significant. In
cially compared to ordinary least squares regression. How- the current analysis, the continuous variables were found to
ever, a number of assumptions still apply. One of these is a have non-linear logits. As a solution, these variables were
linear relationship between the independents and the log divided into different categories according to standard equal
odds (logit) of the dependent. intervals using landing NOD and accident data. The vari-
The Box-Tidwell transformation test was used to check ables then were converted into categorical ones with these
whether all continuous variables met this assumption different levels, each being a separate logit independent
(Garson, 1998). This involved adding to the model interac- variable.
Takeoff Overrun - Most Significant Anomalies
80%
70%
% of Total for Event Type
60%
50%
40%
30%
20%
10%
0%
AT- TO
SysF- SysF- SysF- W- Low W- H- Inc.
W- Rain W- Gusts H- Other R- Wet Rej. @
Tire Power Other Visib. Xwind Planning
HS
All 9.8% 10.9% 20.7% 16.3% 12.0% 15.2% 12.0% 38.0% 12.0% 12.0% 67.4%
Acc 7.3% 9.1% 16.4% 25.5% 14.5% 21.8% 18.2% 40.0% 20.0% 16.4% 69.1%
Inc 13.5% 13.5% 27.0% 2.7% 8.1% 5.4% 2.7% 35.1% 0.0% 5.4% 64.9%
Anomaly
Figure 16. Most frequent anomalies (TOOR).
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Table 5. Summary of anomalies for aircraft overruns
and undershoots.
LDOR LDUS TOOR
Anomaly
ACC INC ACC INC ACC INC
Brake system failure X X
Power failure X
Tire failure X
Other aircraft system fault X X X
Rain X X X X X
Low Visibility X X X X X
Low Ceiling X
Tailwind X X
Crosswind X X X X
Wind shear X
Gusts X X X
Improper flight planning X X X X X X
Visual illusion X
Other human errors X X X X
Wet runway X X X
Contaminated runway X X
Long touchdown X X
High speed during approach X X
Low speed during approach X
Approach too low X X
Other approach anomalies X
Runway construction X
Rejected takeoff at high speed X X
A test for multicollinearity is required for multivariate serious, all variables were kept in the multivariate model, and
logistic regression. Collinearity among the predictor variables caution was applied in interpreting the results. This is preferred
was assessed by conducting linear regression analyses to ob- to the alternative solution of removing variables, which would
tain the relevant tolerance and Variance Inflation Factor (VIF) lead to model misspecification.
values. None of the tolerance values were smaller than 1, and Although the R2 for the models ranged between 0.148 and
no VIF value was greater than 10, suggesting that collinearity 0.245, as shown in Table 8, relatively low values are the norm
among the variables is not serious (Myers, 1990; Menard, in logistic regression (Ash and Schwartz, 1999), and they
2001). Kendall's Tau also was used to assess potential correla- should not be compared with the R2 of linear regressions
tions between predictor variables that are likely to be related. (Hosmer and Lemeshow, 2000). The analysis of models using
Two pairs of variables had Kendall's Tau correlation coeffi- Receiver Operating Characteristic (ROC) curves to classify
cient between 0.51 and 0.60, indicating moderate correlation: flights as "accident" or "normal" suggests good to excellent
equipment class with airport hub size and icing conditions classification accuracy for such models (C-Statistic from
with frozen precipitation. Since none of the correlations were 0.819 to 0.872).
Form of Cumulative Probability Distribution
1
Normal CPD
CPD with Under-reporting
0.8
Fraction of Events
0.6
0.4
0.2
0
0 20 40 60 80 100
Distance Travelled
Figure 17. Schematic form of cumulative distribution
functions.
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Table 6. Summary results for under-reported incidents.
Total # of Total # of % Unreported Estimated #
Accidents and Incidents Incidents ** Unreported
Incidents Incidents
LDOR 240 121 28.8% 17
LDUS 81 38 9.6% 7
TOOR 75 28 28.8% * 1
Note: * value assumed based on comparisons with LDOR
** based on incidents occurring at small distances from threshold
Due to the case-control set-up of the study, the constant the total sampled normal operation population is 242,420
(intercept) term b0 of the final formula must be adjusted to flights,
account for the different sampling fractions between the cases
t0 = 242420/630792133 = 3.843 × 10-4
and the controls. The following formula was used for this
purpose (Hosmer and Lemeshow, 2000): With t1 and t0, the adjusted intercepts of each of the risk
model formula can be calculated:
b*0 = ln(t1/t0) + b0 (5)
b*0 = ln(t1/t0) + b0 = ln(t1/3.843 × 10-4) + b0 = 7.864 + b0 (6)
where
Where b*0 is the original intercept, t1 is the sampling frac-
b*0 = the original intercept,
tion of cases, t0 is the sampling fraction of controls, and b0 is
t1 = the sampling fraction of cases,
the adjusted intercept. The calculated parameters for each
t0 = the sampling fraction of controls, and
model are shown on Table 9.
b0 = s the adjusted intercept.
Using the adjusted intercepts, the final frequency models
Although parameter t1 is normally one when relevant in- are the following:
formation is available for all events, it was necessary to adjust
these values to reflect under-reporting of incidents. Landing Overrun (7)
From the NOD sampling exercise, it was calculated that the
b = -15.456 + 0.551(HeavyAcft ) - 2.113(CommuterAcft )
total number of relevant normal operations from 2000 to 2005
-1.064( MediumAcft ) - 0.876(SmallAcft )
inclusive is 191,902,290. That is 44.78 percent of the period's
+0.44
45(TurbopropAcft ) - 0.857(ForeignOD)
total itinerant operations excluding military operations. From
+1.832(CeilingHeight < 1000 ft )
the TAF, the total number of itinerant operations from 1982
+1.639(CeilingHeight1001 - 2500 ft )
to 2002 inclusive (the accident sampling period) excluding
+2.428(Visibility < 2SM ) + 1.186(Visibility 2 - 4SM )
military operations was computed to be 1,408,495,828 move-
+1.741(Visibility 4 - 6SM ) + 0.322(Visibility 6 - 8SM )
ments. Of the latter, 44.78 percent equates 630,792,133 move-
-0.532(Crosswind 2 - 5knts) + 1.566(Crosswind5 - 12knts)
ments. A detailed description on the calculation of relevant
+1.518(Crosswind > 12knts) + 0.986(ElectStorm)
terminal area forecast traffic is presented in Appendix J. Since
+1.926(IcingConditions) + 1.499(Snow ) - 1.009(Temp < 5C )
-0.631(Temp5 - 15C ) + 0.265(Temp > 25C )
Table 7. Independent variables used +1.006(NonhubApt ) + 0.924(SignificantTerrain)
for frequency models.
Variable LDOR LDUS TOOR Table 8. Summary statistics
Aircraft Weight/Size X X X for frequency models.
Aircraft user class X X
Ceiling X X X Model R2 C
Visibility X X X LDOR 0.245 0.872
Fog X X LDUS 0.199 0.819
Crosswind X X TOOR 0.148 0.861
Gusts
Icing Conditions X X X
Snow X X X Table 9. Calculated model intercepts.
Rain X
Temperature X X X Type of Sampling Original Adjusted
Electrical Storm X Event Fraction (t1) Intercept (b*0) Intercept (b0)
Turboprop/Jet X LDOR 0.938274 -7.656 -15.45637
Foreign Origin/Destination X X LDUS 0.943765 -7.158 -14.96421
Hub/Non-hub airport X TOOR 0.997447 -8.790 -16.65153
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Landing Undershoot (8) Takeoff Overrun (9)
b = -14.9642 + 0.036(HeavyAcft ) - 1.699(CommuterAcft ) b = -16.6515 + 0.721(HeavyAcft ) - 0.619(CommuterAcft )
-0.427( MediumAcft ) + 1.760(SmallAcft ) -0.009(MediumAcft ) + 1.669(SmallAcft ) + 1.336(UserClass1)
+0.288(UserClass1) + 0.908(UserClass 2) - 1.042(ForeignOD) +1.052(UserClass 2) + 1.225(CeilingHeight < 1000 ft )
+0.199(CeilingHeight < 1000 ft ) +1.497(CeilingHeight1001 - 2500 ft )
+1.463(
(CeilingHeight1001 - 2500 ft ) +0.201(Visibility < 2SM ) - 1.941(Visibility 2 - 4SM )
+2.074(Visibility < 2SM ) + 0.069(Visibility 2 - 4SM ) -0.366(Visibility 4 - 6SM ) + 0.317(Visibility 6 - 8SM )
-0.185(Visibility 4 - 6SM ) - 0.295(Visibility 6 - 8SM ) +1.660(Fog ) - 0.292( Xwind 2 - 5knts)
+1.830(Fog ) - 1.705(Rain) - 0.505(Temp 12)
-0.874(Temp5 - 15C ) - 0.446(Temp > 25C ) -0.536(Temp < 5C ) - 0.507(Temp5 - 15C )
+2.815(Icing ) + 2.412(Snow ) +0.502(Temp p > 25C ) + 1.805(Icing ) + 2.567(Snow )
Where:
Equipment Class Ref: C Large jet of MTOW 41k-255k lb (B737, A320 etc.)
HeavyAcft AB Heavy jets of MTOW 255k lb+
Large commuter of MTOW 41k-255k lb (small RJs,
CommuterAcft D ATR42 etc.)
Medium aircraft of MTOW 12.5k-41k lb (biz jets,
MediumAcft E Embraer 120 Learjet 35 etc.)
Small aircraft of MTOW 12.5k or less (small, single or
SmallAcft F twin engine Beech90, Cessna Caravan etc.)
User Class Ref: C = Commercial
UserClass1 F = Cargo
UserClass2 G = GA
ForeignOD Foreign origin/destination (yes/no) - Ref: domestic
CeilingHeight Ref: >2500ft
CeilingHeight<1000ft <1000
CeilingHeight1001-
2500ft 1001-2500
Visibility Ref: 8-10 statute miles (SM)
Visibility<2SM < 2 SM
Visibility2-4SM 2-4 SM
Visibility4-6SM 4-6 SM
Visibility6-8SM 6-8 SM
Crosswind Ref:< 2 knots
Xwind2-5knts 2-5 knots
Xwind5-12knts 5-12 knots
Xwind>12knts >12
ElectStorm Electrical storm (yes/no) Ref: no
IcingConditions Icing conditions (yes/no) Ref: no
Snow Snow (yes/no) Ref: no
Air Temperature Ref: 15 25 deg.C
Temp<5C < 5 deg.C
Temp5-15C 5 15 deg.C
Temp>25C > 25 deg.C
NonhubApt Non-hub airport (yes/no) Ref: hub airport
SignificantTerrain Significant terrain (yes/no) Ref: no
Notes:
Ref: indicates the reference category against which the odds ratios should be interpreted.
Non-hub airport: airport having less than 0.05% of annual passenger boardings
Significant terrain: terrain within the plan view of airport exceeds 4,000 feet above the airport
elevation, or if the terrain within a 6.0 nautical mile radius of the Airport Reference Point rises
to at least 2,000 feet above the airport elevation.
