Blocking a Box-Behnken Design
main topic  

When the number of runs is too large to be completed under steady state conditions, you need to be concerned with the error that may be introduced into the experiment. Running an experiment in blocks allows you to 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 Box-Behnken design, the number of ways to block a design depends on the number of factors. All of the blocked designs have orthogonal blocks. When you are creating a design, Minitab displays the appropriate choices. A design with:

·    Three factors cannot be blocked

·    Four factors can be run in three blocks

·    Five, six, seven, or ten factors can be run in two blocks

·    Nine factors can be run in five or ten blocks

If you add replicates to your design, you can also block on replicates. How this works depends on whether you have blocks in your design.

·    If your design does not have blocks, Minitab places each set of replicates in separate blocks.

·    If your design 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 stays the same.

·    If your design includes blocks but you do not block 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 stays the same.