Interface - The Journal of Wheel/Rail Interaction

WHEEL/RAIL INTERFACE

Applying Quality Concepts to the Wheel/Rail Interface (continued)

In order to prevent sample size from influencing the statistical test result, the proper number of required samples should be calculated before testing begins. Many statistical software packages will calculate the correct sample size based on desired inputs. These inputs usually include the amount of difference to be detected (the practically significant difference), the allowable risk for not detecting a difference when one really does exist, and the standard deviation. Be aware that there is a cost to obtaining and analyzing data, and that taking the correct number of samples is the best way to minimize this cost.

Norfolk Southern has found that a type of statistical analysis called a “split-plot experiment” is often needed in wheel/rail testing. Split-plot experiments originated as a means to compare different agricultural practices, which is a good place to begin an explanation. If I have a garden and I want to see which of two types of seeds and two types of fertilizers produces the best plants, I could subdivide my garden into four equal areas, or plots, and use one type of seed and one type of fertilizer in each area (see Figure 2). I can then measure the plant yield in each plot. However, I cannot determine whether the plant yields in a plot are the result of the seed/fertilizer combination in that particular plot or the result of some characteristic of that particular plot itself. One or more of the plots may have different soil conditions or receive more sunlight and water than the other plots. The only way that the effects of the seed and the fertilizer can be isolated from the effect of the plot is to further subdivide the garden.

Figure 3 shows each of these plots divided into four sub-plots; the seed and fertilizer has also been varied within each plot. Since I will have a plant yield measurement from each sub-plot, I now have 16 total measurements instead of the four that I had before. Now there are enough measurements to separate the effects of the seeds, the fertilizers, and the plot.

What does this have to do with the wheel/rail interface?

Suppose you want to compare how rail from two different manufacturers wears in track. You could put a piece of rail from manufacturer A in one curve and a piece from manufacturer B in another curve on the same track. In doing so, however, you would not be able to say with certainty whether any difference in wear was due to the rail manufacturer or to some difference between the two track locations. If, however, you put a piece of rail from each manufacture at both track locations (each location is a plot), you could start to attribute how much of the difference in wear was due to the manufacturer and how much was due to the track location. An even better test would be to create subplots (entry spiral, full body, and exit spiral) in each curve with multiple rails from each manufacture randomly placed in each subplot.

For an even more complicated example of a split-plot experiment, consider a truck test that NS recently ran. We equipped each of six cars in a test train with a different type of truck. Then we ran the test train through our test site, which consisted of a lateral force site in two back-to-back curves. We had two measurements for each truck in each curve: the lead measurement and the trail measurement. In effect, each run is a garden, each curve is a plot, each car is a sub-plot and each truck is a sub-sub-plot (see Figure 4).

Since NS also wanted to determine whether the direction of travel affected the truck performance measurements, we wound up with the complicated experiment shown in Figure 5. There are eight gardens for each travel direction. From the experimental setup, there are 192 measurements to analyze, which is enough to separate all of the different factors from each other if the analysis is done properly. The standard statistical analysis for this problem — an ANOVA — would give an incorrect answer because it assumes that the degrees of freedom are the same for all factors. But the degrees of freedom for each variable are not the same in a split-plot experiment. As a result, a modified ANOVA must be used to get the correct answer. Again, it is important to ensure that the data meets the underlying assumptions of the statistical test.

There are a number of ways to make mistakes during data analysis that can cause the analyst to draw an incorrect conclusion. The analyst must gather the correct amount of data, use the correct statistical tests, and verify that assumptions for each test are met in order to draw a correct practical conclusion.

Stephen S. Woody is Manager, Track Inspection & Development, Norfolk Southern.

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