Multistratum fractional factorial designs (Q2799891)

In this chapter, the author summarizes the theory of multistratum fractional factorial designs, i.e., designs with multiple sources of error. The theory of multistratum designs includes in a unique framework several pre-existing models widely used in applications, and therefore it is a powerful tool in data analysis of fractional factorial designs. Examples of blocked full-factorial designs, split-plot designs, and split-lot designs are used to illustrate how randomization restrictions can arise in practice.NEWLINENEWLINEThe randomization restrictions affect data analysis of a linear model of the form \(y = X\beta + \varepsilon\) in the error term, since the components of the error term \(\varepsilon\) depend on the randomization structure, and the covariance matrix of the response variable \(y\) is not proportional to the identity matrix. This issue is illustrated with full details in a couple of examples. The first part of the analysis is devoted to full-factorial designs, and then some methods for choosing fractional factorial designs in that setting are presented.NEWLINENEWLINEFor the entire collection see [Zbl 1327.62001].