1. Factorial Design
Full Factorial
Design
Factors: 3
Base Design:
3, 8
Runs: 21
Replicates:
2
Blocks: none
Center pts
(total): 5
Factor Name
Low High
A Fill Rate
(RPM) 20 80
B Ramp Rate
5 75
C Suck Back
2 50
All terms are free
from aliasing
Data Matrix (randomized)
Run A B C
1 0 0 0
2 0 0 0
3 + - -
4 - + +
5 + - -
6 + + -
7 0 0 0
8 0 0 0
9 0 0 0
10 + - +
11 - - +
12 + + +
13 - - -
14 - + +
15 - + -
16 - + -
17 - - +

2. 18 - - -
19 + - +
20 + + -
21 + + +
Factorial Fit: Means of rep versus Fill Rate (R, Ramp Rate, Suck Back
Estimated Effects and Coefficients for Means of repeats (coded units)
Term Effect Coef SE Coef T P
Constant 2.7674 0.007729 358.06 0.000
Fill Rate (RPM) -0.0579 -0.0289 0.007729 -3.74 0.003
Ramp Rate -0.0148 -0.0074 0.007729 -0.96 0.358
Suck Back -0.7130 -0.3565 0.007729 -46.13 0.000
Fill Rate (RPM)*Ramp Rate -0.0242 -0.0121 0.007729 -1.56 0.144
Fill Rate (RPM)*Suck Back 0.0345 0.0172 0.007729 2.23 0.046
Ramp Rate*Suck Back -0.0082 -0.0041 0.007729 -0.53 0.604
Fill Rate (RPM)*Ramp Rate*Suck Back 0.0174 0.0087 0.007729 1.12 0.283
Ct Pt -0.0619 0.015840 -3.90 0.002
S = 0.0309159 R-Sq = 99.45% R-Sq(adj) = 99.08%
Analysis of Variance for Means of repeats (coded units)
Estimated Coefficients for Means of repeats using data in uncoded units
Term Coef
Constant 3.19539
Fill Rate (RPM) -7.68041E-04
Ramp Rate 0.000939980
Suck Back -0.0151664

3. Fill Rate (RPM)*Ramp Rate -2.04752E-05
Fill Rate (RPM)*Suck Back 1.01513E-05
Ramp Rate*Suck Back -2.21329E-05
Fill Rate (RPM)*Ramp Rate*Suck Back 3.44742E-07
Ct Pt -0.0618525
Effects Pareto for Means of repeats
Alias Structure
I
Fill Rate (RPM)
Ramp Rate
Suck Back
Fill Rate (RPM)*Ramp Rate
Fill Rate (RPM)*Suck Back
Ramp Rate*Suck Back
Fill Rate (RPM)*Ramp Rate*Suck Back
Source DF Seq SS Adj SS Adj MS F P
Main Effects 3 2.04789 2.04789 0.682630 714.20 0.000
2-Way Interactions 3 0.00736 0.00736 0.002454 2.57 0.103
3-Way Interactions 1 0.00121 0.00121 0.001208 1.26 0.283
Curvature 1 0.01457 0.01457 0.014574 15.25 0.002
Residual Error 12 0.01147 0.01147 0.000956
Pure Error 12 0.01147 0.01147 0.000956
Total 20 2.08250
Unusual Observations for Means of repeats
Means
of
Obs StdOrder repeats Fit SE Fit Residual St Resid
7 20 2.63580 2.70556 0.01383 -0.06976 -2.52R
R denotes an observation with a large standardized residual.

4. Term
St andardized Effect
BC
B
ABC
AB
AC
A
C
50403020100
2.18
Factor Name
A Fill Rate (RPM)
B Ramp Rate
C Suck Back
Pareto Chart of the Standardized Effects
(response is Means of repeats, Alpha = .05)
Reduced Model
Factorial Fit: Means of repeats versus Fill Rate (RPM), Suck Back
Estimated Effects and Coefficients for Means of repeats (coded units)
Term Effect Coef SE Coef T P
Constant 2.7674 0.007945 348.33 0.000
Fill Rate (RPM) -0.0579 -0.0289 0.007945 -3.64 0.002
Suck Back -0.7130 -0.3565 0.007945 -44.87 0.000
Fill Rate (RPM)*Suck Back 0.0345 0.0172 0.007945 2.17 0.045
Ct Pt -0.0619 0.016282 -3.80 0.002

5. S = 0.0317791 R-Sq = 99.22% R-Sq(adj) = 99.03%
Analysis of Variance for Means of repeats (coded units)
Source DF Seq SS Adj SS Adj MS F P
Main Effects 2 2.04702 2.04702 1.02351 1013.46 0.000
2-Way Interactions 1 0.00475 0.00475 0.00475 4.71 0.045
Curvature 1 0.01457 0.01457 0.01457 14.43 0.002
Residual Error 16 0.01616 0.01616 0.00101
Pure Error 16 0.01616 0.01616 0.00101
Total 20 2.08250
Unusual Observations for Means of repeats
Means
Estimated Coefficients for Means of repeats using data in uncoded units
Term Coef
Constant 3.23299
Fill Rate (RPM) -0.00158705
Suck Back -0.0160517
Fill Rate (RPM)*Suck Back 2.39410E-05
Ct Pt -0.0618525
Effects Pareto for Means of repeats
Alias Structure
I
Fill Rate (RPM)
Suck Back
Fill Rate (RPM)*Suck Back
of
Obs StdOrder repeats Fit SE Fit Residual St Resid
7 20 2.63580 2.70556 0.01421 -0.06976 -2.45R
R denotes an observation with a large standardized residual.

6. Term
St andardized Effect
AC
A
C
50403020100
2.12
Factor Name
A Fill Rate (RPM)
C Suck Back
Pareto Chart of the Standardized Effects
(response is Means of repeats, Alpha = .05)

7. Residual
Percent
0.080.040.00-0.04-0.08
99
90
50
10
1
Fitted Value
Residual
3.23.02.82.62.4
0.06
0.03
0.00
-0.03
-0.06
Residual
Frequency
0.060.040.020.00-0.02-0.04-0.06
6.0
4.5
3.0
1.5
0.0
Obser vation Or der
Residual
2018161412108642
0.06
0.03
0.00
-0.03
-0.06
Normal Probabilit y Plot of t he Residuals Residuals Versus t he Fit t ed Values
Hist ogram of t he Residuals Residuals Versus t he Order of t he Dat a
Residual Plots for Means of repeats

8. MeanofMeansofrepeats
805020
3.2
3.1
3.0
2.9
2.8
2.7
2.6
2.5
2.4
50262
Fill Rate (RPM) Suck Back Point Type
Corner
Center
Main Effects Plot (data means) for Means of repeats

9. MeanofMeansofrepeats
805020
3.2
3.0
2.8
2.6
2.4
75405
50262
3.2
3.0
2.8
2.6
2.4
Fill Rate (RPM) Ramp Rate
Suck Back
Point Type
Corner
Center
Main Effects Plot (data means) for Means of repeats

10. Suck Back
Mean
50262
3.2
3.1
3.0
2.9
2.8
2.7
2.6
2.5
2.4
2.3
Fill
50 Center
80 Corner
Rate
(RPM) Point Type
20 Corner
I nteraction Plot (data means) for Means of repeats

11. Fill Rat e ( RPM )
Ram p Rat e
Suck Back
75405 50262
3.00
2.75
2.50
3.00
2.75
2.50
Fill
50 Center
80 Corner
Rate
(RPM) Point Type
20 Corner
Ramp
40 Center
75 Corner
Rate Point Type
5 Corner
I nteraction Plot (data means) for Means of repeats

12. 50
2
8020
Suck Back
Fill Rate (RPM)
2.70556
2.39920
3.077753.17010
2.42260
Centerpoint
Factorial Point
Cube Plot (data means) for Means of repeats

13. 50
2
75
5
8020
Suck Back
Ramp Rate
Fill Rate (RPM)
2.70556
2.38430
2.414102.43070
2.41450
3.05370
3.101803.15260
3.18760
Centerpoint
Factorial Point
Cube Plot (data means) for Means of repeats
Response Surface Regression: Means of rep versus Fill Rate (R, Ramp Rate, ...
The following terms cannot be estimated, and were removed.
Ramp Rate*Ramp Rate
Suck Back*Suck Back
The analysis was done using coded units.
Estimated Regression Coefficients for Means of repeats
Term Coef SE Coef T P
Constant 2.70556 0.013965 193.733 0.000
Fill Rate (RPM) -0.02894 0.007807 -3.707 0.003
Ramp Rate -0.00739 0.007807 -0.946 0.361

14. Suck Back -0.35651 0.007807 -45.666 0.000
Fill Rate (RPM)*Fill Rate (RPM) 0.06185 0.015999 3.866 0.002
Fill Rate (RPM)*Ramp Rate -0.01209 0.007807 -1.548 0.146
Fill Rate (RPM)*Suck Back 0.01724 0.007807 2.208 0.046
Ramp Rate*Suck Back -0.00411 0.007807 -0.527 0.607
S = 0.03123 R-Sq = 99.4% R-Sq(adj) = 99.1%
Analysis of Variance for Means of repeats
Source DF Seq SS Adj SS Adj MS F P
Regression 7 2.06983 2.06983 0.295690 303.22 0.000
Linear 3 2.04789 2.04789 0.682630 700.02 0.000
Square 1 0.01457 0.01457 0.014574 14.95 0.002
Interaction 3 0.00736 0.00736 0.002454 2.52 0.104
Residual Error 13 0.01268 0.01268 0.000975
Lack-of-Fit 1 0.00121 0.00121 0.001208 1.26 0.283
Pure Error 12 0.01147 0.01147 0.000956
Total 20 2.08250
Unusual Observations for Means of repeats
Estimated Regression Coefficients for Means of repeats using data in uncoded units
Term Coef
Constant 3.32327
Fill Rate (RPM) -0.00799907
Ramp Rate 0.000491815
Suck Back -0.0158559
Fill Rate (RPM)*Fill Rate (RPM) 6.87250E-05
Fill Rate (RPM)*Ramp Rate -1.15119E-05
Fill Rate (RPM)*Suck Back 2.39410E-05
Ramp Rate*Suck Back -4.89583E-06
Means
of
Obs StdOrder repeats Fit SE Fit Residual St Resid
7 20 2.636 2.706 0.014 -0.070 -2.50 R
R denotes an observation with a large standardized residual.
Reduced Model

15. Response Surface Regression: Means of repeats versus Fill Rate (RPM), Suck Back
The following terms cannot be estimated, and were removed.
Suck Back*Suck Back
The analysis was done using coded units.
Estimated Regression Coefficients for Means of repeats
Term Coef SE Coef T P
Constant 2.70556 0.014212 190.371 0.000
Fill Rate (RPM) -0.02894 0.007945 -3.642 0.002
Suck Back -0.35651 0.007945 -44.874 0.000
Fill Rate (RPM)*Fill Rate (RPM) 0.06185 0.016282 3.799 0.002
Fill Rate (RPM)*Suck Back 0.01724 0.007945 2.170 0.045
S = 0.03178 R-Sq = 99.2% R-Sq(adj) = 99.0%
Analysis of Variance for Means of repeats
Source DF Seq SS Adj SS Adj MS F P
Regression 4 2.06634 2.06634 0.51659 511.52 0.000
Linear 2 2.04702 2.04702 1.02351 1013.46 0.000
Square 1 0.01457 0.01457 0.01457 14.43 0.002
Interaction 1 0.00475 0.00475 0.00475 4.71 0.045
Residual Error 16 0.01616 0.01616 0.00101
Pure Error 16 0.01616 0.01616 0.00101
Total 20 2.08250
Unusual Observations for Means of repeats
Means
of
Obs StdOrder repeats Fit SE Fit Residual St Resid
7 20 2.636 2.706 0.014 -0.070 -2.45 R
R denotes an observation with a large standardized residual.
Estimated Regression Coefficients for Means of repeats using data in uncoded units
Term Coef
Constant 3.34295
Fill Rate (RPM) -0.00845955

16. Suck Back -0.0160517
Fill Rate (RPM)*Fill Rate (RPM) 6.87250E-05
Fill Rate (RPM)*Suck Back 2.39410E-05
80
60
Means of r epeats
2.50
2.75
3.00
3.25
Fill Rate ( RPM)400
15 2030 45
Suck Back
Surface Plot of Means of repeats vs Fill Rate (RPM), Suck Back

17. Suck Back
FillRate(RPM)
5040302010
80
70
60
50
40
30
20
Means of
2.55 - 2.70
2.70 - 2.85
2.85
repeats
- 3.00
3.00 - 3.15
> 3.15
< 2.40
2.40 - 2.55
Contour Plot of Means of repeats vs Fill Rate (RPM), Suck Back
Reduced Model
Response Surface Regression: Means of repeats versus Fill Rate (RPM), Suck Back
The analysis was done using coded units.
Estimated Regression Coefficients for Means of repeats
Term Coef SE Coef T P
Constant 2.70556 0.014212 190.371 0.000
Fill Rate (RPM) -0.02894 0.007945 -3.642 0.002
Suck Back -0.35651 0.007945 -44.874 0.000
Fill Rate (RPM)*Fill Rate (RPM) 0.06185 0.016282 3.799 0.002

18. Fill Rate (RPM)*Suck Back 0.01724 0.007945 2.170 0.045
S = 0.03178 R-Sq = 99.2% R-Sq(adj) = 99.0%
Analysis of Variance for Means of repeats
Source DF Seq SS Adj SS Adj MS F P
Regression 4 2.06634 2.06634 0.51659 511.52 0.000
Linear 2 2.04702 2.04702 1.02351 1013.46 0.000
Square 1 0.01457 0.01457 0.01457 14.43 0.002
Interaction 1 0.00475 0.00475 0.00475 4.71 0.045
Residual Error 16 0.01616 0.01616 0.00101
Pure Error 16 0.01616 0.01616 0.00101
Total 20 2.08250
Unusual Observations for Means of repeats
Means
of
Obs StdOrder repeats Fit SE Fit Residual St Resid
7 20 2.636 2.706 0.014 -0.070 -2.45 R
R denotes an observation with a large standardized residual.
Estimated Regression Coefficients for Means of repeats using data in uncoded units
Term Coef
Constant 3.34295
Fill Rate (RPM) -0.00845955
Suck Back -0.0160517
Fill Rate (RPM)*Fill Rate (RPM) 6.87250E-05
Fill Rate (RPM)*Suck Back 2.39410E-05
Equation for the Model = 3.34295 – 0.00845955 Fill Rate (RPM) – 0.0160517 Suck Back + 6.87250E-05
Fill Rate (RPM)*Fill Rate (RPM) + 2.39410E-05 Fill Rate (RPM)*Suck Back
One-way ANOVA: Avg4, Avg3, Avg2, Avg1
Source DF SS MS F P
Factor 3 0.0234 0.0078 0.08 0.971
Error 78 7.6049 0.0975
Total 81 7.6283

19. S = 0.3122 R-Sq = 0.31% R-Sq(adj) = 0.00%
Individual 95% CIs For Mean Based on
Pooled StDev
Level N Mean StDev ---+---------+---------+---------+------
Avg4 21 2.7256 0.3146 (-------------*------------)
Avg3 20 2.7124 0.3064 (-------------*-------------)
Avg2 20 2.7384 0.3050 (-------------*-------------)
Avg1 21 2.7580 0.3221 (-------------*------------)
---+---------+---------+---------+------
2.60 2.70 2.80 2.90
Pooled StDev = 0.3122
Dat a
Frequency
3.43.23.02.82.62.42.22.0
3.0
2.5
2.0
1.5
1.0
0.5
0.0
Mean
2.738 0.3050 20
2.758 0.3221 21
StDev N
2.726 0.3146 21
2.712 0.3064 20
Variable
Avg4
Avg3
Avg2
Avg1
Histogram of Avg4, Avg3, Avg2, Avg1
Normal