Nonregular factorial and supersaturated designs (Q2799892)

In this chapter, the author describes the theory of nonregular fractional factorial designs, starting from the analysis of the aliasing structure through the general expression of the regression model. While in regular designs the contrasts are either orthogonal or fully aliased, the situation becomes much more complicated in the case of nonregular designs. Therefore, criteria of optimality for choosing factorial designs are needed. In that direction, the major optimality criteria used in applications are described. In particular, the generalized minimum aberration and the minimum moment aberration are discussed, and necessary and sufficient conditions for optimality are stated. Generalized resolution and uniform designs are briefly introduced.NEWLINENEWLINEIn this chapter, also supersaturated designs are analyzed. Supersaturated designs are designs where the number of runs is less than the number of parameters of interest. The notion of optimality is adapted to this framework and some optimality criteria are given.NEWLINENEWLINEFor the entire collection see [Zbl 1327.62001].