generating full-factorial models in minitab we want to generate a design for a 2 3 full factorial...
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Generating Full-Factorial Models in Minitab
We want to generate a design for a 23 full factorial model.
2 x 2 x 2 = 8 runs
We want to generate a design for a 23 full factorial model.
2 x 2 x 2 = 8 runs
Click on down arrow and select number of
factors. For this example it’s 3.
Click on down arrow and select number of
factors. For this example it’s 3.
Highlight desired design from list. For 3 factors, there are
two options.
Highlight desired design from list. For 3 factors, there are
two options.
Enter 2 replicates. Enter 2 replicates.
Generating Full-Factorial Models in Minitab
After selecting the design, you can name the factors (X’s)and define their low and high values
Click on Factors button
Generating Full-Factorial Models in Minitab
After entering your factors,Click on the Options button
& De-Select the “Randomize runs”
Then click “OK”twice
…What Do You See
Notice Minitab gives you the values you need to run your experiment—not –1 and +1.
Since we didn’trandomize and we made StartAngle factor C,we only need tochange startangle once.
It is recommended to RANDOMIZE
YOUR EXPERIMENTNotes:
1) A new worksheet will be created for the design.
2) The Minitab default is to randomize the run order.
For our Design
Analyzing the Results of the DOE: Step 9
Let’s look at some graphs
Analyzing the Results of the DOE: Step 9
Click on the doublearrow button to transferall available terms intoselected terms
Make sure you have “Distance” in the Responses box
Perform these stepsin both setup—Main Effects & Interactions
Analyzing the Results of the DOE: Step 9
It looks like Start Angle and Pin Position had a big effecton our Y--Distance
Analyzing the Results of the DOE: Step 9
Since the lines are nearly parallel, the two-way interactions will probably be insignificant
Analyzing the Results of the DOE: Step 9
Go to Stat>DOE>Analyze Factorial Design
Analyzing the Results of the DOE: Step 9
2. Click on Graphs
3. Then Pareto withAlpha = 0.05
4. Finally click Ok
1. Put Distance in Responses:
3. Click on these 3 Plots
Analyzing the Results of the DOE: Step 9
1. Then click on Storage
2. Select Fits & Residuals
3. Then Ok and Ok
Analyzing the Results of the DOE: Step 9
These 3 graphs give you a good idea about what’s going on
Analyzing the Results of the DOE: Steps 10 & 11
Steps 10 & 11: Plot & Interpret the Residuals• Residuals are the difference between the actual Y value and the Y
value predicted by the regression equation.• Residuals should
» be randomly and normally distributed about a mean of zero» not correlate with the predicted Y» not exhibit trends over time (if data chronological)
• Stat > DOE > Analyze Factorial Design, Graphs button» Select
normal plot of residualsresiduals against fitsresiduals against order
• Any trends or patterns in the residual plots indicates inadequacies in the regression model, such as missing Xs or nonlinear relationships.
Analyzing the Results of the DOE: Steps 10 & 11
Let’s look at each graph individually
Analyzing the Results of the DOE: Steps 10 & 11
But first lets perform a Normality test on The residuals by going to:Stat>Basic Statistics>Normality Test
In variable, select RESI1
Then click Ok
Analyzing the Results of the DOE: Steps 10 & 11
-3 -2 -1 0 1 2 3
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Nor
ma
l Sco
re
Residual
Normal Probability Plot of the Residuals(response is Distance)
Average: 0.0000000StDev: 1.49443N: 16
Anderson-Darling Normality TestA-Squared: 0.322P-Value: 0.497
-2 0 2
.001
.01
.05
.20
.50
.80
.95
.99
.999
Pro
babi
lity
RESI1
Normal Probability Plot
Residuals Look normal
P-value: 0.497
If residuals are not normal, your modelmay not predict very well
Analyzing the Results of the DOE: Steps 10 & 11
2 4 6 8 10 12 14 16
-3
-2
-1
0
1
2
3
Observation Order
Res
idua
l
Residuals Versus the Order of the Data(response is Distance)
No trends in this graph
Analyzing the Results of the DOE: Steps 10 & 11
100 110 120 130 140 150 160 170 180 190
-3
-2
-1
0
1
2
3
Fitted Value
Res
idua
l
Residuals Versus the Fitted Values(response is Distance)
This graph indicates there might be more variability in the smaller distances, but with only two reps, we’ll press on!
Analyzing the Results of the DOE: Step 12Examine the Factor Effects
We’ll keepAnything withA low P-value
Lower than 0.05
Since we’re keeping the 3-way interaction, we need to include stop position in the model
Analyzing the Results of the DOE: Step 12Examine the Factor Effects
Go back in Stat>DOE>Analyze Factorial Design and click on Terms, then remove the two-way interactions
Put 2-wayinteractionsback in Available Terms
Step 13: Develop Prediction Models
Coefficients for theCoded model
Coefficients for the Uncoded model
Y = 145.4 – 11.3A + 0.7B + 29.2C –1.31ABC
Y = -339.4 – 9.4A + 2.9B + 2.9C
For the Coded Model
Y = 145.4 – 11.3A + 0.7B + 29.2C –1.31ABCY = 145.4 – 11.3A + 0.7B + 29.2C –1.31ABC
145 = 145.4 – 11.3 (Pin Position) + 0.7(Stop Position) + 29.2(Start Angle) – 1.3(ABC)
• Let’s just arbitrarily set A & B to some value since they are discrete
Set Pin Position to 0 (coded) which equates to 2 (actual: what you set in your design)
Stop Position at –1 (coded) which equates to 2 (actual: what you set in your design)
• Let’s figure out Start Angle
145 = 145.4 – 11.3(0) + 0.7(-1) + 29.2 (Start Angle) – 1.31(0*-1*C)
145 = 145.4 – 0 – 0.7 + 29.2(Start Angle) - 0
145 – 145.4 + 0.7 = 29.2(Start Angle)
0.3 = 29.2(Start Angle)
0.01 = Start Angle
Converting from the coded units:
160 180
-1 +1
170
0
170.1
0.01
For the Un-coded Model
Y = -339.4 – 9.4A + 2.9B + 2.9C –0.0ABCY = -339.4 – 9.4A + 2.9B + 2.9C –0.0ABC
145 = -339.4 – 9.4 (Pin Position) + 2.9(Stop Position) + 2.9(Start Angle)
• Let’s just arbitrarily set A & B to some value since they are discrete
Set Pin Position to 2
Stop Position at 2
• Let’s figure out Start Angle
145 = -339.4 – 9.4(2) + 2.9(2) + 2.9(Start Angle)
145 = -339.4 – 18.8 + 5.8 + 2.9(Start Angle)
497.4 = 2.9(Start Angle)
497.4 / 2.9 = (Start Angle)
171.5 = Start Angle