Adding center points
main topic 

Adding center points to a factorial design may allow you to detect curvature in the fitted data. If there is curvature that involves the center of the design, the response at the center point will be either higher or lower than the fitted value of the factorial (corner) points.

The way Minitab adds center points to the design depends on whether you have text, numeric, or a combination of text and numeric factors. Here is how Minitab adds center points:

·    When all factors are numeric and the design is:

-    Not blocked, Minitab adds the specified number of center points to the design.

-    Blocked, Minitab adds the specified number of center points to each block.

·    When all of the factors in a design are text, you cannot add center points.

·    When you have a combination of numeric and text factors, there is no true center to the design. In this case, center points are called pseudo-center points. When the design is:

-    Not blocked, Minitab adds the specified number of center points for each combination of the levels of the text factors. In total, for Q text factors, Minitab adds 2Q times as many centerpoints.

-    Blocked, Minitab adds the specified number of center points for each combination of the levels of the text factors to each block. In each block, for Q text factors, Minitab adds 2Q times as many centerpoints.

For example, consider an unblocked 23 design. Factors A and C are numeric with levels 0, 10 and .2, .3, respectively. Factor B is text indicating whether a catalyst is present or absent. If you specify 3 center points in the Designs subdialog box, Minitab adds a total of 2 x 3 = 6 pseudo-center points, three points for the low level of factor B and three for the high level. These six points are:

Next, consider a blocked 25 design where three factors are text, and there are two blocks. There are 2 x 2 x 2 = 8 combinations of text levels. If you specify two center points per block, Minitab will add 8 x 2 = 16 pseudo-center points to each of the two blocks.