–100 Catapult Exercises
Lightning Calculator, 2002
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.
addition to serving as a DOE teaching tool, the Catapult
can be used to teach several additional concepts as
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:
back distance of the catapult arm.
Attaching point of the elastic on the upright.
Attaching point of the elastic on the throwing arm.
position on the throwing arm.
5. Tilt of
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.
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.
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).
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
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
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.