Statapult - Worked DOE Example

Statapult – Case Study In our Statapult example, we conducted a full-factorial experiment with three factors - Pull Back Angle, Hook Position and Peg Position. An eight-run design with two levels for each factor was performed.

The Statapult was fired three times for each combination and in-flight distances were recorded. The control factors and constant factors are shown in the following illustration.

The table below summarizes the results for each experimental run.

Run Pull Back Hook Peg Distance Distance Distance

1 140 1 1 45.5 46 46

2 140 1 3 33 34 34

3 140 3 1 38 36.5 36.5

4 140 3 3 26 26.5 26

5 160 1 1 74 71 73

6 160 1 3 54 55.5 55

7 160 3 1 56 54 55

8 160 3 3 43 44 44 The Pareto Chart shows vertical bars with heights proportional to the average delta or average delta/2 values for each factor and interaction. Pareto analysis is often used to rank order the most important factors and interactions in an experiment.

The Pareto Chart for “Distance Average Delta/2" is shown here. This Pareto Chart indicates that Pull Back has the most impact on the flight distance and the interaction between Pull Back, Hook and Peg has the least impact.

Pareto Chart 12 10.438 10

8 -6.5208 6 -5.6458

2 -1.5625 0.97917 -0.77083 0.64583 0 Pull Back(A) Peg(C) Hook(B) AB BC AC ABC Factors

The Main Effects Plot is a plot of the average of the data points at the low factor setting and the average of the data points at the high factor setting. The greater the slope, the more significant the effect.

Here is the Main Effects Plot for Pull Back, Hook Position, Peg Position and the Pull Back/Hook interaction term.

Main Effects 80

20 140(-) 160(+) 1(-) 3(+) 1(-) 3(+) -1(-) 1(+) Pull Back(A) Hook(B) Peg(C) AB Factors An interaction occurs when the difference in the response between the levels of one factor is not the same at all levels of the other factors. The result produced by the individual factor is different than the result produced by the combination of two or more factors. If the slopes of the lines on the interaction plot are not equal, there may be some interaction.

Here is the interaction graph for our experiment.

Interactions 80

Hook(-) Peg(-)

Hook(+) Peg(+) 44 Peg(-)

32 Peg(+)

20 140(-) 160(+) 140(-) 160(+) 1(-) 3(+) Pull Back(A) Pull Back(A) Hook(B) Factors

Contour Plots are projections of lines of constant response from the response surface onto the two dimensional “factor” plane. Contour Plots provide the ability to graphically “see” those factor settings that give a specific response. By properly interpreting this graph, students can predict how to set up the Statapult in order to “hit” a specific distance.

Here is the Contour Plot for our experiment. The Peg Position was set to 1 for this particular plot. In this case, we asked the students to hit a target of 55 inches. The students used the following set-up: Pull Back Angle 152 Hook 2 Peg 1

Response Surface Plots are similar to Contour Plots except on a three dimensional plane. Response Surface Plots provide the ability to graphically “see,” on a three dimensional plane, those factor settings that give a specific response.

The Response Surface Plot for our experiment is shown below. The Peg Position was set to 1 for this particular plot.

DOE Wisdom software will allow the user to change which factors are on the x and y axis and also change the set value of the constant factor. Another nice feature of DOE Wisdom is it allows the user to rotate the Response Surface Plot.

NOTE: To purchase the software, contact Launsby Consulting at 719-282-1143.

So far we have only discussed graphical methods for interpreting the data. Analysis of Variance (ANOVA) is a statistical technique for analyzing data that tests for a difference between two or more means by comparing the variances “within” groups and variances “between” groups. The ANOVA for our experiment is shown here. The ANOVA can be used to generate a model for our Statapult experiment. Remember, this model is in terms of coded values. The model for our experiment is:

All terms were left in the model because the P(2 Tail) values were all less than 0.10. This model can now be used to evaluate any combinations of Pull Back Angles, Hook Positions and Peg Positions and predict the distance the ball would be launched.

Software can do these calculations for you. DOE Wisdom has a “hit a target” feature. Open the Stats folder. Under the View pull down menu, select Prediction Equation. On the Prediction Equation toolbar, click on the Find Target button. The following window will appear.

In this example, our response is Distance. The software can show the best settings to minimize the flight distance, maximize the flight distance or hit a specific flight distance. We want to set up the Statapult so it will hit a target of 43 inches. We entered this value in the target field. Click on the Search button and the following Window will appear:

This indicates that we can hit a target of 43 inches by setting the factors as follows:

Pull Back Angle 147 Hook 2 Peg 2

We conducted four confirmation runs using these settings and obtained the following results:

43, 42.5, 43.5, 42

The confirmation runs confirm our prediction model and that the proper settings have been determined. We are ready to start shooting at more targets.

NOTE: Actual models will vary from one Statapult to the next.