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30 Appendix M provides the results for multivariate logistic use weight factors to reduce model bias, particularly for mod- regression analysis used to obtain the model coefficients eling the tail of the probability distribution. Therefore the described earlier. model can be represented by the following equation: P{Location > y} = e - bym (11) Accident Location Models where Based on the accident/incident data for wreckage loca- P{Location>y} = the probability the overrun/undershoot tions, three sets of complementary cumulative probability distance from the runway centerline is distribution (CCPD) models were developed in this study. greater than y (P{Location<=0} = c); With CCPDs, the fraction of accidents involving locations y = a given location or distance beyond the exceeding a given distance from the runway end or thresh- threshold; and old can be estimated. When the CCPD is multiplied by the b, m = regression coefficients. frequency of accident occurrence, a complementary cumu- lative frequency distribution (CCFD) is obtained. The latter The correlations between the overrun and undershoot dis- quantifies the overall frequency of accidents involving loca- tances to the lateral distance relative to the runway axis also tions exceeding a given distance from the runway end or were evaluated for assessing the correlation between x and y threshold. locations. A high correlation would suggest the best geome- The CCPD model structure selected was used by Eddowes try for RSAs is not a rectangle. et al. (2001) and is in the following form: When plotting the percent of accidents beyond a certain For the longitudinal distribution, the basic model is: distance from the threshold, shown in Figure 18, it can be noted that an RSA with 1000 ft in length will encompass close P{Location > x} = e - axn (10) to 95 percent of all landing overruns. It should be noted that where the raw data includes reported accidents and incidents, but incidents were weighted to account for unreported cases. P{Location > x} = the probability the overrun/undershoot Figure 19 depicts the distribution of raw lateral distances distance along the runway centerline from the extended runway centerline. For many events the beyond the threshold is greater than x; distance was very close to the runway centerline and the x = a given location or distance beyond the actual distance was not reported. For such cases when possi- threshold; and ble, the y-distance was assumed to be 0.0. As mentioned a, n = regression coefficients. earlier, weighting factors were used to obtain unbiased esti- For the transverse distribution, the same model structure mates at the tails of the distribution. In this case, weighting was selected. However, given the accidents transverse loca- was applied to the events having y-distances above 400 ft. tion is not reported, in general, if the wreckage location is The LDOR CCPD for normalized distances is shown in within the extended runway lateral limits, it was necessary to Figures 20 and 21. Using transformed distances, a 1000 ft-long Raw Distances Model for Landing Overruns 100% Actual Raw Distances Raw Distances Model 80% P{d>x}=exp(-0.003871*x^0.955175) Prob{distance > x ) % R2=99.8%; n=257 60% 40% 20% 0% 0 500 1000 1500 2000 2500 Distance x from Threshold Figure 18. LDOR location model using raw (nonnormalized) distances.

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31 Raw Lateral Distances Model for LDOR 100% Actual Data Model 80% Probaility{distance > y} P{d>x}=exp(-0.20174*C2^0.489009) R2=94.7%; n=141 60% 40% 20% 0% 0 200 400 600 800 1000 1200 Distance Y from Extended Runway Axis (ft) Figure 19. LDOR lateral location model using raw (nonnormalized) distances. Normalized Distances Model for Landing Overruns 100% Actual Data Norm Model Raw Model 80% Prob{distance > x} P{d>x}=exp(-0.004692*B2^0.824513) R2=99.5%; n=232 60% 40% 20% 0% 0 1000 2000 3000 4000 5000 6000 Distance x from Threshold (ft) Figure 20. LDOR location model using normalized distances. Normalized Lateral Distances Model for LDOR 100% Actual Data Model Probaility{distance > y} 80% P{d>x}=exp(-0.243692*Y^0.388726) R2=93.4%; n=138 60% 40% 20% 0% 0 500 1000 1500 2000 2500 Distance Y from Extended Runway Axis (ft) Figure 21. LDOR lateral location model using normalized distances.