Central Composite Design (CCD)

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Here’s a representation of a classic central composite design for 2 factors.

  • Four corners of the square represent the factorial (+/- 1) design points
  • Four star points represent the axial (+/- alpha) design points
  • Replicated center point

Numeric Factors: The number of numeric factors involved in the experiment

Categoric Factors: The number of categoric factors involved in the experiment

Note

For CCD’s the number of runs required for the numeric factors will be multiplied by the number of categoric combinations. If two categoric factors having three levels each are added to this design the number of runs will be multiplied by nine. Consider optimal designs when you have both numeric and categoric factors.

Enter factor ranges in terms of …

+/-1 to define the limits for the area of interest where the optimum is believed to exist. Axial points will typically be outside this limit. Enter the limits in the Low and High columns.

alphas to ensure that even the extreme axial runs are within the area of operability. The area of interest must be within the area of operability. Enter the limits in the -alpha and +alpha columns.

Type: There will be different options available in this pull down based on how many factors are to be included in the experiment. The designs listed here form the factorial core of the central composite design. The default suggestion is the largest fraction that will produce a design under 1000 runs or maintain at least resolution V behavior. Smaller fractional cores can be used to save on the budget. For six or more factors we recommend using the Min Run Res V type to get both good estimates while keeping the number of runs under control. Small designs are the smallest recognized central composite design and are not recommended due to possible analysis issues.

Blocks: Central composite designs can be split into blocks. The factorial design is split into sub-fractions that support the two-factor interaction model and the axial points in the final block if needed.

Options button: Click on the options button to change the axial (alpha) distance which is how far the star points will be from the center in coded units. Use the help button on the options dialog for more information.

The Points area provides a preview of the number and type of runs that will be in the design.