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15 Table 2. Adjustment factors used to correct required distances. Local Factor Unit Reference Adjustment Elevation (E) (i) 1000 ft E = 0 ft (sea level) Fe = 0.07 x E + 1 Temperature (T) (i) deg C T = 15 deg C Ft = 0.01 x (T (15 1.981 E) + 1 Tailwind (TWLDJ) for knot TWLDJ = 0 knot FTWJ = (RD + 22 x TWLDJ)/RD (ii) Jets (iii) Tailwind (TWLDT) for knot TWLDT = 0 knot FTWJ = (RD + 30 x TWLDT)/RD Turboprops (iii) Headwind (HWTOJ) for knot HWTOJ = 0 knot FTWJ = (RD + 6 x HWTOJ)/RD Jets (iii) Headwind (HWTOT) for knot HWTOJ = 0 knot FTWJ = (RD + 6 x HWTOT)/RD Turboprops (iii) Runway Surface Condition Yes/No Dry FW = 1.4 Wet (W) (iv) Runway Surface Condition Yes/No Dry FS = 1.6 Snow (S) (iv) Runway Surface Condition Yes/No Dry FSl = 2.0 Slush (Sl) (iv) Runway Surface Condition Yes/No Dry FI = 3.5 Ice (I) (iv) i RD is the runway distance required in feet ii temperature and elevation corrections used for runway design iii correction for wind are average values for aircraft type (jet or turboprop) iv runway contamination factors are those suggested by Flight Safety Foundation were entered by blocks, each consisting of related factors, such curves were defined for each model to calculate the C-value. that the change in the model's substantive significance could An example of this assessment is shown in Figure 16 repre- be observed as the variables were included. Table 3 summarizes senting the model for landing overruns. The area under the the model coefficients obtained for each model. curve for this model represents the C-value and is 87.4%. The Table 4 summarizes the parameters representing the ac- C-values for each of the five models developed were above curacy of each model obtained. The table presents the R2 78% and are considered excellent models. and C-values for each model. It is important to note that rel- The cut-off point is the critical probability above which the atively low R2 values are the norm in logistic regression (Ash model will class an event as an accident. The ROC curve plots and Schwartz 1999) and they should not be compared with all potential cut-off points according to their respective True the R2 of linear regressions (Hosmer and Lemeshow 2000). Positive Rates and False Positive Rates. The best cut-off point A better parameter to assess the predictive capability of a has an optimally high sensitivity and specificity. logistic model is the C-value. This parameter represents the area under the sensitivity/specificity curve for the model, Event Location Models which is known as Receiver Operating Characteristic (ROC) curve. The accident location models are based on historical acci- Sensitivity and specificity are statistical measures of the per- dent data for aircraft overruns, veer-offs, and undershoots. formance of a binary classification test. Sensitivity measures The accident location for overruns depends on the type of ter- the proportion of true positives that are correctly identified as rain (paved or unpaved) and if EMAS is installed in the RSA. such (the percentage of accidents and incidents that are cor- When EMAS is available, during landing and takeoff over- rectly identified when using the model). Specificity measures runs, the aircraft will stop at shorter distances, and typical de- the proportion of true negatives that are correctly identified celeration for the type of aircraft is used to assess the location (the percentage of normal operations that the model can cor- probability. rectly identify as non-incident). These two measures are closely Worldwide data on accidents and incidents were used to related to the concepts of Type I and Type II errors. A theoret- develop the location models. The model structure is similar to ical, optimal prediction can achieve 100% sensitivity (i.e., pre- the one used by Eddowes et al. (2001). Based on the accident/ dict all incidents) and 100% specificity (i.e., not predict a incident location data, five sets of complementary cumulative normal operation as an incident). A perfect model has a C-value probability distribution (CCPD) models were developed. With equal to 1.00. CCPDs, the fraction of accidents involving locations exceeding To assess how successful the models are in classifying flights a given distance from the runway end or threshold can be esti- correctly as "accident" or "normal" and to find the appropri- mated. When the CCPD is multiplied by the frequency of ac- ate cut-off points for the logistic regression models, the ROC cident occurrence, a complementary cumulative frequency

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16 Table 3. Independent variables used for frequency models. Variable LDOR LDUS LDVO TOOR TOVO Adjusted Constant -13.065 -15.378 -13.088 -14.293 -15.612 User Class F 1.693 1.266 User Class G 1.539 1.288 1.682 2.094 User Class T/C -0.498 0.017 Aircraft Class A/B -1.013 -0.778 -0.770 -1.150 -0.852 Aircraft Class D/E/F 0.935 0.138 -0.252 -2.108 -0.091 Ceiling less than 200 ft -0.019 0.070 0.792 Ceiling 200 to 1000 ft -0.772 -1.144 -0.114 Ceiling 1000 to 2500 ft -0.345 -0.721 Visibility less than 2 SM 2.881 3.096 2.143 1.364 2.042 Visibility from 2 to 4 SM 1.532 1.824 -0.334 0.808 Visibility from 4 to 8 SM 0.200 0.416 0.652 -1.500 Xwind from 5 to 12 kt -0.913 -0.295 0.653 -0.695 0.102 Xwind from 2 to 5 kt -1.342 -0.698 -0.091 -1.045 Xwind more than 12 kt -0.921 -1.166 2.192 0.219 0.706 Tailwind from 5 to 12 kt 0.066 Tailwind more than 12 kt 0.786 0.98 Temp less than 5 C 0.043 0.197 0.558 0.269 0.988 Temp from 5 to 15 C -0.019 -0.71 -0.453 -0.544 -0.42 Temp more than 25 C -1.067 -0.463 0.291 0.315 -0.921 Icing Conditions 2.007 2.703 2.67 3.324 Rain 0.991 -0.126 0.355 -1.541 Snow 0.449 -0.25 0.548 0.721 0.963 Frozen Precipitation -0.103 Gusts 0.041 -0.036 0.006 Fog 1.74 Thunderstorm -1.344 Turboprop -2.517 0.56 1.522 Foreign OD 0.929 1.354 -0.334 -0.236 Hub/Non-Hub Airport 1.334 -0.692 Log Criticality Factor 9.237 1.629 4.318 1.707 Night Conditions -1.36 Where: Ref: Equipment Class C Large jet of MTOW 41k-255k lb (B737, A320 etc.) Heavy Acft AB Heavy jets of MTOW 255k lb+ (B777, A340, etc.) Large commuter of MTOW 41k-255k lb (Regional Jets, Commuter Acft D ERJ-190, CRJ-900, ATR42, etc.) Medium aircraft of MTOW 12.5k-41k lb (biz jets, Medium Acft E Embraer 120, Learjet 35 etc.) Small Acft F Small aircraft of MTOW 12.5k or less (small, Beech-90, Cessna Caravan, etc.) User Class Ref: C = Commercial User Class F Cargo User Class T/C Taxi/Commuter User Class G General Aviation Foreign OD Foreign origin/destination (yes/no) - Ref: domestic Ceiling (feet) Ref: Ceiling Height > 2500 ft Visibility (Statute Miles) Ref: Visibility > 8 SM Crosswind (knots) Ref: Crosswind < 2 kt Tailwind (knots) Ref: Tailwind < 5 kt Gusts (knots) Ref: No gusts Thunderstorms (yes/no) Ref: No thunderstorms Icing Conditions (yes/no) Ref: No icing conditions Snow (yes/no) Ref: No snow Rain (yes/no) Ref: No rain Fog (yes/no) Ref: No fog Air Temperature (deg C) Ref: Air temperature above 15 C and below 25C Non-Hub Airport (yes/no) Ref: Hub airport Log Criticality Factor If Log(CF) > 0, available runway distance is smaller than required distance 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.

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17 Table 4. Summary statistics for frequency models. x Model R2 C LDOR 0.28 0.87 y LDUS 0.14 0.85 LDVO 0.32 0.88 TOOR 0.11 0.78 TOVO 0.14 0.82 Figure 17. X-Y origin for aircraft overruns. distribution (CCFD) is obtained. The latter quantifies the over- For the transverse distribution, the same model structure all frequency of accidents involving locations exceeding a given was selected. However, given the accident's transverse loca- distance from the runway boundaries. tion for aircraft overruns and undershoots, in general, is Figures 17 to 19 show the axis locations used to represent not reported if the wreckage location is within the extended each type of incident. The reference location of the aircraft is runway lateral limits, it was necessary to use weight factors to its nose wheel. For overruns and undershoots, the x-y origin reduce model bias, particularly for modeling the tail of the is the centerline at the runway end. For veer-offs, the y-axis probability distribution. The model can be represented by the origin is the edge of the runway, not necessarily the edge of the following equation: paved area when the runway has shoulders. For the longitudinal distribution, the basic model is: P { Location > y } = e - bym P { Location > x } = e - axn where P{Location>y} = the probability the overrun/undershoot where distance from the runway border (veer- P{Location > x} = the probability the overrun/undershoot offs) or centerline (overruns and under- distance along the runway centerline be- shoots) is greater than y; yond the runway end is greater than x; y = a given location or distance from the x = a given location or distance beyond the extended runway centerline or runway runway end; and border; and a, n = regression coefficients. b, m = regression coefficients. A typical longitudinal location distribution is presented in A typical transverse location distribution is presented in Figure 20. Figure 21, and the model parameters are presented in Table 5. Figure 16. ROC curve for LDOR frequency model.