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 ...

Two fractional factorial designs are called isomorphic if one can be obtained from the other by relabeling the factors, reordering the runs, and switching the levels of factors. To identify the isomorphism of two s-factor n-run designs is known to be an NP hard problem, when n and s increase. There is no tractable algorithm for the identification of isomorphic designs. In this paper, we propose...

Multicomponent interventions composed of behavioral, delivery, or implementation factors in addition to medications are becoming increasingly common in health sciences. A natural experimental approach to developing and refining such multicomponent interventions is to start with a large number of potential components and screen out the least active ones. Factorial designs can be used efficiently...

Nonregular fractional factorial designs such as Plackett-Burman designs and other orthogonal arrays are widely used in various screening experiments for their run size economy and flexibility. The traditional analysis focuses on main effects only. Hamada and Wu (1992) went beyond the traditional approach and proposed an analysis strategy to demonstrate that some interactions could be entertaine...

An A-optimal minimax design criterion is proposed to construct fractional factorial designs, which extends the study of the D-optimal minimax design criterion in Lin and Zhou (Canadian Journal of Statistics 41, 325–340, 2013). The resulting Aoptimal and D-optimal minimax designs minimize, respectively, the maximum trace and determinant of the mean squared error matrix of the least squares estim...

Fractional factorial designs are classified into two broad types: regular designs and nonregular designs. Regular designs are constructed through defining relations among factors; they are introduced in Chapter 1 (Section 1.7) and fully described in Chapter 7. These designs have a simple alias structure in that any two factorial contrasts are either orthogonal or fully aliased. The run sizes ar...