Flight Tack Data Analysis to estimate the height of aircraft over the Perimeter Taxiway System
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- Normal Distribution Tests
| DFW SOUTH FLOW RUNWAY 18R
1340 ARRIVALS 0 100 200 300 400 500 600 1 224 447 670 893 1116 1339 NUMBER OF ARRIVALS H E IG H T A B O V E R U N WA Y DATA
M EAN UCL
LCL
Figure 3 Runway 18R arrival data scatter plot Table 5 shows the confidence intervals for the mean over flight height at the centerline of the PT. The small variation in the arrival paths decreases the widths of their confidence intervals.
Satyamurti and Mattingly
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Table 5 Confidence Bounds for the Mean Heights Runway Arrival/ Departure Mean Standard Deviation Confidence Bounds Lower (95%) Upper (95%) 17C
Arrival 260
39.7 258
262 18R
Arrival 255
41.0 253
257 35C
Arrival 206
32.0 204
208 36L
Arrival 209
26.6 207
210 17R
Departure 1260
294 1245
1270 18L
Departure 1200
277 1186
1212 35L
Departure 1340
318 1326
1356 36R
Departure 1370
285 1357
1386 Normal Distribution Tests The researchers have interest in determining if the height data is normally distributed or may be approximated by the Normal distribution in order to assess the risk posed by aircraft flying over the PT. The Chi-square goodness-of-fit test is used to test whether the distribution of a data set follows a particular pattern, in this case the normal distribution. The goodness-of-fit test is a hypothesis test with the following hypotheses: H 0
H A : The data do not follow the normal distribution Before computing a Chi-square test statistic, the height data must be standardized (z-value) by subtracting the mean and dividing each value by the standard deviation. Then, the height data is divided into ten bins of z-values as shown in Table 6. The corresponding normal probabilities and expected number of height observations for each runway dataset are computed. A sample Chi-square test statistic computation for one runway is shown in Table 6. TABLE 6. Runway 18R Arrival Height Chi-square Test Z value Observed count Normal Prob Exp Count (Ob-Ex) χ 2 (<-2.0) 8 0.023 31 -23
16.90 (-2.0, -1.5) 47 0.044
59 -12
2.43 (-1.5, -1.0) 133 0.092
123 10 0.77 (-1.0, -0.5) 247
0.150 201
46 10.53
(-0.5, 0.0) 270
0.191 256
14 0.77
(0.0, 0.5) 304
0.191 256
48 9.02
(0.5, 1.0) 142
0.150 201
-59 17.32
(1.0, 1.5) 105
0.092 123
-18 2.71
(1.5,2.0) 38 0.044 59 -21
7.45 (>2.0)
46 0.023
31 15 7.48 1340 1 1340 75.37
Table 7 displays the results of the Chi-square test for the eight runways at DFW under study. The height data for runway 35L is normally distributed based on the Chi-square test while the remaining runways cannot reject the Chi-square test at a 95% significance level. The runways that cannot be proven to be normally distributed appear to have similar anomalies to those
Satyamurti and Mattingly
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8 observed in Table 6 where more of the data is concentrated in the middle and beyond the UCL as shown in Figure 3. While the height data for most of the runways is not normally distributed, the types of anomalies that prevent their distributions from being classified as normal make the assumption of normality conservative when considering the lower end of the distribution. In the next section, this assumption will be made for the risk analysis related to flying over the PT. Table 7 Chi-square Test Results Runway Observations Test Statistic Rejection Boundary ( = .05) Result
17C 1363
133 16.9
Reject H 0
17R 2155
67.8 16.9
Reject H 0
18L 1730
33.8 16.9
Reject H 0
18R 1340
75.4 16.9
Reject H 0
35C 1276
50.6 16.9
Reject H 0
35L 1652
8.6 16.9
Fail to Reject H 0
36L 1086
47.8 16.9
Reject H 0
36R 1475
25.7 16.9
Reject H 0
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