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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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23 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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24 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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25 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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26 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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27 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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28 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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29 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.