8.  Examples

8.1  Example 1: Applying the Sliding Scale Analysis

The following example illustrates how the sliding scale analysis is applied to the expected crash rates by homogeneous highway segment and plotted.

Given:

• W = 500 ft.,
• n = 5,
• and I = W/n = 100ft.

Figure 3.shows a plot of predicted crashes/yr for a highway 1200 ft. long

Figure 3.  Histogram of Predicted Crashes for Example Highway by Station

The first point is plotted at the midpoint of the first segment (W) and will be 250 ft. away from the beginning of the highway. The predicted crashes/yr are calculated as follows:

• @250 (midpoint of 0 to 500), plot average of 1st 5 intervals = (3+4+2+3+5)/5 = 3.4

Likewise, the next seven points are:

• @350 (midpoint of 100 to 600), plot average of intervals 2-6 = (4+2+3+5+4)/5 = 3.6
• @450 (midpoint of 200 to 700), plot average of intervals 3-7 = (2+3+5+4+2)/5 = 3.2
• @550 (midpoint of 300 to 800), plot average of intervals 4-8 = (3+5+4+2+6)/5 = 4.0
• @650 (midpoint of 400 to 900), plot average of intervals 5-9 = (5+4+2+6+4)/5 = 4.2
• @750 (midpoint of 500 to 1000), plot average of intervals 6-10 = (4+2+6+4+3)/5 = 3.8
• @850 (midpoint of 600 to 1100), plot average of intervals 7-11 = (2+6+4+3+5)/5 = 4.0
• @950 (midpoint of 700 to 1200), plot average of intervals 8-12 = (6+4+3+5+3)/5 = 4.2

These points are plotted in Figure Ex.3.2. The end points were not calculated since for the remaining points n < 5. Therefore, the average for the remaining points are found as follows:

• @50 (midpoint of -200 to 300), plot average of intervals 1-3 = (3+4+2)/3 = 3.0
• @150 (midpoint of -100 to 400), plot average of intervals 1-4 = (3+4+2+3)/4 = 3.0
• @1050 (midpoint of 800 to 1300), plot average of intervals 9-12 = (4+3+5+3)/4 = 3.75
• @1150 (midpoint of 900 to 1400), plot average of intervals 10-12 = (3+5+3)/3 = 3.67

Figure 4.  Crash Fequency Plot of Example Highway with End Sections by Station Sliding Scale (No Endpoints)

The complete sliding scale plot for this example is shown in Figure 5.

Figure 5.  Crash Fequency Plot of Example Highway with End Sections by Station Sliding Scale (With Endpoints)