Add axial points

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