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# CAT –100 Catapult Exercises

**Copyright Lightning Calculator, 2014**

**Catapult History**

In ancient times the catapult was used to hurl objects at the enemy. This catapult is used to teach designed experiments or Taguchi Methods. The unit is produced for classroom use to allow students to conduct an experiment and determine the best combination of tilt, spring direction, draw back distance, ball position, and ball type for overcoming the enemy. The catapult experiment can turn a dull statistics class into a fun and learning exercise.

In addition to serving as a DOE teaching tool, the Catapult can be used to teach several additional concepts as described below

Description

The catapult throws a variety of balls a distance across the classroom. The distance is the response variable in the experiment (total distance less than 100 inches). Students can vary a total of six factors, each at three levels, in conducting the experiment. The factors are:

1. Draw back distance of the catapult arm.

2. Attaching point of the elastic on the upright.

3. Attaching point of the elastic on the throwing arm.

4. Ball position on the throwing arm.

5. Tilt of the catapult.

6. Ball type.

E**xercises**

1. Form a team to operate with the catapult. Give them a tape measure, one of the balls (instructors choice) and the catapult that has been previously set up. They can use no other equipment and can make no adjustments to the catapult. Each person gets five shots to be taken in sequence with no delays. The distance from the catapult to the landing spot is recorded. Rotate through the team members to get approximately 100 measurements. Have the team assemble the data in a suitable format and compare it to a specification, e.g. 8 inches, which is arbitrarily set by the instructor. Save the data in a time series format for analysis and note which individual is associated with each data set.

2. Create a process analysis team (could be same team) to flow chart the process, list potential improvement ideas (however adjustments to the catapult are not permitted), and then repeat exercise 1. The instructor may want to provide other methods to improve the measurement capability, e.g. masking tape for the floor, talcum powder to dust the ball with prior to throwing so that it will mark the floor, aluminum foil for the landing area so that marks can be made on the foil, etc. Insist that the most accurate readings be taken, i.e. to 1/16 of an inch. Compare the data generated from the two experiments.

3. Develop histograms of the data from exercise 1 and 2 and analyze the data either manually or with software. Additional statistical measures can be determined for the data like a run chart, mean, standard deviation, median, quartiles, scatter chart, etc. Ask them to determine what the process specification should be based on the data.

4. Create a cause and effect diagram of factors that affect throwing distance. Which of the factors are noise versus controllable factors? Pull back distance would be the controllable factor and noise factors would include things like, variability in the elastic (rubber hysterious), variability in the speed of pull back of the arm, measurement error in being able to read to the nearest 1/16 of an inch, etc.

5. Check the data in exercise 1 and 2 for normality with normal probability paper or software calculations. Determine if there are any outliers.

6. Use the yields from data from exercise 3 to determine the process yields and calculate the process sigma if it is being used in a Six Sigma training session.

7. Use the data from exercise 1 and 2 and plot an average and range chart to show the impact of the process changes from exercise 1 to 2. Calculate a process Cp and Cpk given the specifications by the instructor and then the calculated specification based on the results of exercise 3

8. Use the catapult to develop a Failure Mode and Effects Analysis. The instructor should arbitrarily assign a consequence to things like, what happens if the elastic breaks, what happens if the ball drops out of the holder on the arm, the direction / location of the target area (what happens if we fire in the wrong direction).

9. Use hypothesis testing to compare data sets from exercise 1 and 2 and any other additional exercises created by the instructor. (The instructor may change the setup of the catapult and then determine if there is a significant difference in the setup based on the data). Develop confidence intervals for the data comparisons. Convert the data to attribute data, e.g. good and bad (in spec and out of spec) and analyze the data again based on the percent defective.

10. Set up a screen type of designed experiment with each of the factors at two levels. A one-half or one-quarter fractional factorial experiment can be used to determine which factors are the most significant.

11. Once the most significant factors are determined in exercise 10 conduct a full factorial experiment run at three levels for the most critical factors in order to determine the optimum experimental settings.

12. Based on the results of experiment 11 calculate the expected results from the experimental design formula (this is provided in most software programs). Conduct a confirming experiment to confirm the expected results with all of the factors set at their optimum levels. Compare the results from both the calculated and actual experiment.

13. Set up a Taguchi experiment with an orthogonal array. Try an L8 or an L18 depending on the numbers your desire to test two versus three levels and the ability to calculate interactions. Lead a discussion about what possible interactions you would want to test for and which columns in the orthogonal array you would assign to the interactions. Compare the results from the Taguchi approach versus the traditional approach.

*Note: See CAT-100 Demonstration for a Statistical Analysis of a Fractional Factorial Experiment. *