ABSTRACT
In this chapter we extend the design and analysis of multi-stratum complete factorial experiments discussed in Chapter 13 to regular fractional factorial designs. Independent treatment factorial effects are chosen to define regular fractions and to partition the treatment combinations into disjoint classes for different levels of various unit factors in a given block structure. This general procedure is applied to several specific cases, including fractional factorial designs for blocked, split-plot, and strip-plot experiments. The issue of design selection is also addressed. For unstructured experimental units, minimum aberration is a popular criterion for selecting fractional factorial designs under the hierarchical assumption. This criterion is extended to fractional factorial experiments with multiple strata. In addition to effect aliasing, stratum variances are also taken into account in the design selection. The examples in Chapter 1 are revisited.
