| Overview
In this ALT, you conduct and analyze a fractional factorial experiment
using Jenga Blocks, a game produced by Milton-Bradley Inc. You and
your team stack the Jenga Blocks - one at a time and long side down
- on a small flat wooden platform. The stacking proceeds until the
tower tumbles over. The number of blocks in a stable tower (right
before the tumble) is registered as the height of the tower. The
goal is to maximize the height of the tower.
The experimental process is identical to the one described in Information
Sheet: Introduction to Fractional Factorial Experiments. Teams brainstorm
to identify factors and factor levels that you believe influence
the height of the Jenga towers. You then select three factors for
actual testing via an L-4 array.
After completing this ALT, you should be able to demonstrate the
following competencies:
- Use sound sampling techniques and data analysis to make repeatable,
defensible inferences (Comp. 1).
- Solve real world problems by designing and conducting factorial
and fractional factorial experiments (Comp. 2).
- Graphically display outcomes using simple graphical presentation
methods (Comp. 3).
Materials and Equipment
No materials or equipment are needed to complete this ALT.
Safety and Disposal
No special safety or disposal procedures are required.
Pre-Activity
Design of Experiments – Fractional Factorials
The following example is a simple non-replicated example that looks
at the effects of combining the effects of different fertilizers,
corn hybrids and the amount of water as part of a study to maximize
the bushel yields of corn. Click here
to access the example. And click here
to download its solution.
Additional Information on How to Conduct a Factorial
and Fractional Factorial Experiments
NIST
Section 5.3.3.4
Statsoft
online textbook
Java
Applets
Self Assessment
An experiment has been carried out to determine
the effect of three factors on increasing the viscosity (centipoise)
of the materials during mixing. The three factors are mixing speed
(rpm), mixing time (minutes) and the viscosity of the materials
before mixing (centipoises). A fractional factorial experiment has
been carried out to determine the best settings. Solution is found
on the second sheet (Practice) of the Excel
spreadsheet.
Activity
In your team, perform the following step to complete the activity:
- With your team, brainstorm to identify the factors/levels you
wish to test.
- Refer to Instruction Sheet: On the Block and review it before
continuing.
- Have your facilitator approve your selected factors/levels.
Then, with your team, choose where to place the three factors
in the basic L4 array. Refer to Information Sheet: Introduction
to Fractional Factorial Experiments, page 4.
- Individually complete Data Sheet: Basic L4 Array.
- With your team, run the four trials in the experiment. Refer
to Information Sheet: Introduction to Fractional Factorial Experiments,
page 5.
- Individually complete Data Sheet: Execution Array.
- When finished with the actual testing, collaborate with your
team to formulate a linear model using an analysis array. Refer
to Information Sheet: Introduction to Fractional Factorial Experiments,
page 6.
- Individually complete Data Sheet: Analysis Array.
- Prepare a coefficient bar chart that includes a ranking of factors
in order of importance on the bottom of the chart.
- Prepare an effects diagram, including a proposal of a paper
champion (the optimum value as predicted by the model [equation])
at the bottom of the diagram.
- With your team, run an additional trail to confirm the paper
champion.
Post-Activity
Your team should now post its results from
the activity to the Discussion Board.
Assignment
To prepare for ALT #5: Back to the Block, read pages 51-63 in your
Statistical Experiments Participant Journal, and review
ANOVA sites highlighted in the Pre-Activity for section the next
ALT.
Assessment
Your facilitator may use Assessment Sheet: On the Block to evaluate
your results from the activity and your posting to the Discussion
Board.
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