Stat > DOE > Modify Design > Add axial points > Specify

Add axial points to a design to estimate the square terms for factors. You can add axial points to 2-level factorial designs and Plackett-Burman designs, if those designs have only continuous factors. This modification changes the design from a factorial design to a central composite response surface design. For more information, go to What are response surface designs, central composite designs, and Box-Behnken designs?.

Value of Alpha

Alpha (α) is the distance, in coded units, of each axial point (also called star point) from the center in a central composite design. Alpha, along with the number of center points, determines whether a design can be orthogonally blocked and is rotatable. For more information, go to What is alpha (α) in a central composite design?. Choose one of the following to specify the value of alpha:

  • Default (rotatable if possible): Minitab determines the value of alpha (α) based on the number of corner points in the design. The default value of α provides rotatability whenever possible. Alpha (α) depends on the number of non-center points in the design. The factor values at the axial points are beyond the current high and low levels for the factors.
  • Face Centered: Minitab generates a face-centered design (α=1). The factor values at the axial points are the same as the high and low levels for the factor. Face-centered axial points are common when the high and low values are as extreme as the factors can be. For example, for a certain experiment, the high and low levels for the factors are the most extreme levels that are safe to run. Thus, the engineer who designs the experiment sets the axial points at the current high and low values.
  • Custom: Enter your own α value, in coded units. In coded units, the high and low levels of the factors are +1 and −1. Custom levels are common when the rotatable levels are unfeasible, but values greater than the current high and low levels for the factors are possible. For example, an engineer wants the axial points to be rotatable, but the rotatable levels are so extreme that the settings are not feasible. The engineer enters the maximum feasible value in coded units.
Add the following number of center points (to the axial block)
Enter a positive integer to add center points to the axial block. There are several reasons why you might want to add center points to your design. For more information, go to How Minitab adds center points to a two-level factorial design or Should I include center points in a response surface design?.

Example of adding axial points

For example, an engineer plans a sequential experiment and begins with a 2-level factorial design. The analysis of that design suggests that the relationship between the factors and the response variable has curvature. The engineer then uses Modify Design to add axial points to the design to add runs to model the curvature.

Before modification

C1 C2 C3 C4 C5 C6 C7 C8
StdOrder RunOrder CenterPt Blocks Pressure Injection Cooling Strength
4 1 1 1 150.000 100.000 50.0000 22.7001
1 2 1 1 75.000 85.000 50.0000 5.7349
2 3 1 1 150.000 85.000 25.0000 22.7105
6 4 0 1 112.500 92.500 37.5000 12.8237
7 5 0 1 112.500 92.500 37.5000 18.8239
3 6 1 1 75.000 100.000 25.0000 5.7751
5 7 0 1 112.500 92.500 37.5000 12.8233

After modification

C1 C2 C3 C4 C5 C6 C7 C8
StdOrder RunOrder CenterPt Blocks Pressure Injection Cooling Strength
4 1 1 1 150.000 100.000 50.0000 22.7001
1 2 1 1 75.000 85.000 50.0000 5.7349
2 3 1 1 150.000 85.000 25.0000 22.7105
6 4 0 1 112.500 92.500 37.5000 12.8237
7 5 0 1 112.500 92.500 37.5000 18.8239
3 6 1 1 75.000 100.000 25.0000 5.7751
5 7 0 1 112.500 92.500 37.5000 12.8233
8 8 −1 2 59.467 92.500 37.5000  
9 9 −1 2 165.533 92.500 37.5000  
10 10 −1 2 112.500 81.893 37.5000  
11 11 −1 2 112.500 103.107 37.5000  
12 12 −1 2 112.500 92.500 19.8223  
13 13 −1 2 112.500 92.500 55.1777  

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