formula fueler design of experiments class exercise
DESCRIPTION
There are alternative ways to teach DOE besides using the Statapult (Six Sigma Academy's favorite contraption which cost $300). A $20 toy made by Mattel is an effective teaching aid to full-factorial and fractional DOE's.TRANSCRIPT
Design For Six SigmaDOE – Full Factorial Designs
Class Exercise: Formula Fuelers®
Background Information:• You are going to make
the fuel that powers this motorcycle.
• By experimenting with 3 different liquids, you will control the distance the motorcycle will travel.
• Your objective is to hit a target given to you by your instructor at the end of the experiment.
The Experiment: Full Factorial Design• 3 Factors:
• 2 Levels: – -1 = do not use or absent from fuel tank– 1 = add to fuel tank
• Response Variable:
Liquid A Liquid B Liquid C
Distance to the nearest ¼ inch.
Setting-Up the Experiment in Minitab
Setting-up the Experiment in Minitab
Treatments: How Much of Each Liquid?
A B C A ml
B ml
C ml
Total ml
-1 -1 -1 0 0 0 0
1 -1 -1 6 0 0 6
-1 1 -1 0 6 0 6
1 1 -1 3 3 0 6
-1 -1 1 0 0 6 6
1 -1 1 3 0 3 6
-1 1 1 0 3 3 6
1 1 1 2 2 2 6
Launching the Motorcycle
Push this power button. There will be a 2 second delay.
Response Variable: Measuring Distance
Note: Motorcycle may not follow a straight line!
Top View of Motorcycle
Measure distance from start position to center of front-wheel to the closest 0.25 inch
Sta
rtin
g
Po
siti
on
Procedure For Running Experiment1. With syringe, extract needed amount of liquids
from cups marked A, B, and C.2. Open fuel tank and fill with syringe. Close fuel
tank.3. Snap fuel tank into rear cavity of the Motorcycle.4. Position Motorcycle on Starting Line. Push power
button.5. Wait for the Motorcycle to come to a stop.
Measure the distance it traveled.6. Pick-up Motorcycle. Remove fuel tank.7. Open fuel tank cap and pour out contents.
Team Roles: Who Does What?Task 2 People 3 People 4 People
Pick up motorcycle and remove fuel tank Person 1 Person 3 Person 1
Open cap and pour out the contents in the fuel tank Person 1 Person 1 Person 1
Collect samples of each liquid as specified per observation Person 1 Person 1 Person 2
Pour mixture into fuel tank and close the cap Person 1 Person 1 Person 2
Insert fuel tank into motorcycle Person 2 Person 1 Person 2
Position motorcycle on the floor in starting position Person 2 Person 2 Person 3
Press the power button and wait 2 seconds Person 2 Person 2 Person 3
Watch the vehicle run. Make sure it doesn't hit anything.
When the it stops, take a measurement of how far it traveled Person 2 Person 3 Person 1
Enter the results into Minitab Person 2 Person 3 Person 4
Example of Experiment Data Collected
Analyze Results
Analyze Results
Analyze Results
Term
Standardized Effect
BC
AC
AB
C
B
A
ABC
9080706050403020100
2.12
A Factor AB Factor BC Factor C
Factor Name
Pareto Chart of the Standardized Effects(response is DistInches, Alpha = .05)
Factorial Fit: DistInches versus Factor A, Factor B, Factor C
Estimated Effects and Coefficients for DistInches (coded units)
Term Effect Coef SE Coef T PConstant 86.91 0.3652 237.98 0.000Factor A 47.19 23.59 0.3652 64.61 0.000Factor B 47.02 23.51 0.3652 64.38 0.000Factor C -22.85 -11.43 0.3652 -31.29 0.000Factor A*Factor B -20.35 -10.18 0.3652 -27.87 0.000Factor A*Factor C -5.23 -2.61 0.3652 -7.16 0.000Factor B*Factor C -3.81 -1.91 0.3652 -5.22 0.000Factor A*Factor B*Factor C 60.06 30.03 0.3652 82.24 0.000
S = 1.78900 R-Sq = 99.91% R-Sq(adj) = 99.86%
Analysis of Variance for DistInches (coded units)
Source DF Seq SS Adj SS Adj MS F PMain Effects 3 29759.6 29759.6 9919.9 3099.45 0.0002-Way Interactions 3 2737.0 2737.0 912.3 285.06 0.0003-Way Interactions 1 21645.0 21645.0 21645.0 6762.97 0.000Residual Error 16 51.2 51.2 3.2 Pure Error 16 51.2 51.2 3.2
Analyze Results
Analyze Results
Factor A
1-1 1-1
120
80
40
Factor B
120
80
40
Factor C
-11
Factor A
-11
Factor B
Interaction Plot (fitted means) for DistInches
Do Any of the Lines Intersect?
Mean o
f D
istI
nch
es
1-1
110
100
90
80
70
1-1
1-1
110
100
90
80
70
Factor A Factor B
Factor C
Main Effects Plot (fitted means) for DistInches
Which Factor Has the Steepest Slope?
1
-1
1
-1
1-1
Factor C
Factor B
Factor A
137.917
55.00052.750
56.250
109.750
139.3336.500
137.750
Cube Plot (fitted means) for DistInches
Cube Plots: Determine Settings to Meet Goal
Hitting A TargetObjective:
– The instructor will give each team a number, which represents a distance the team must meet.
– If the motorcycle goes past this mark, the team loses.– The winning team is the one who can come closest to
the mark.– The instructor may take the average of several runs
(e.g., the average distance after 3 attempts)
The target distance for your team is _______ inches.What fuel mixture will you make? (hint: Cube Plot)