Designing fractional factorial split-plot experiments with few whole-plot factors

When it is impractical to perform the experimental runs of a fractional factorial design in a completely random order, restrictions on the randomization can be imposed. The resulting design is said to have a split-plot, or nested, error structure. Similarly to fractional factorials, fractional factorial split-plot designs can be ranked by using the aberration criterion.Techniques that generate the required designs systematically presuppose unreplicated settings of the wholeplot factors. We use a cheese-making experiment to demonstrate the practical relevance of designs with replicated settings of these factors. We create such designs by splitting the whole plots according to one or more subplot effects.We develop a systematic method to generate the required designs and we use the method to create a table of designs that is likely to be useful in practice.