Blocks in a central composite design

When the number of runs is too large to be conducted under steady state conditions, you may introduce error into the experiment. Doing an experiment in blocks lets you separately and independently estimate the block effects (or different experimental conditions) from the factor effects. For example, blocks might be days, suppliers, batches of raw material, machine operators, or manufacturing shift.

For a central composite design, the number of orthogonal blocks depends on the number of factors, the number of runs, and the design fraction you choose. A central composite design can always be separated into a factorial block and an axial point block. With three or more factors, the factorial block can also be split into two or more blocks. When you are creating a design, Minitab displays the appropriate choices.

If you add replicates to your design, you can also block on replicates. How this works depends on whether you have existing blocks in your design.
  • If your design does not already include blocks, Minitab puts each set of replicates in separate blocks.
  • If your design already includes blocks, Minitab replicates the existing blocking scheme. The points in each existing block are replicated to form new blocks. The number of blocks in your design will equal the number of original blocks multiplied by the number of replicates. The number of runs in each block remains the same.
  • If your design already includes blocks but you do not create blocks on replicates, Minitab replicates the points within each block. The total number of runs in the each block equals the number of original runs times the number of replicates. The total number of blocks in the design remains the same.

The value of α, in combination with the number of center points, determines whether a design exhibits the properties of rotatability and orthogonal blocking. Minitab provides default designs that achieve rotatability and orthogonal blocks, when both properties can be achieved at the same time. When the design includes blocks and you cannot achieve both properties at the same time, the default designs includes orthogonal blocks.

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