Fractional factorial experiments

Lewis, Susan Margaret (1977) Fractional factorial experiments. University of Southampton, Doctoral Thesis.

Abstract

Factorial experiments are used to study the effect of simultaneously applying combinations of factors to experimental units. Information on the individual effects of each factor and the way in which the factors interact may be obtained. If only a small number of experimental units is available a fraction of all the possible combinations of factor levels may be used. This results in aliasing of the factorial effects. Useful fractions of factorial experiments have the important factorial effects aliased with effects which are assumed to be negligible. This thesis describes methods of constructing such fractions. Methods of constructing fractions of asymmetrical factorial experiments have been based previously on proportional frequency conditions. Some problems associated with estimating main effects in these fractions are discussed. A family of fractions constructed as the initial block of a single replicate factorial experiment arranged in a generalized cyclic design is studied. These fractions consist of a group of treatment combinations. A general theory is developed including rules for determining the aliasing scheme. The orthogonality of all estimable effects in these fractions is established and a simple method of arranging the fractions in blocks is given. Tables of resolution III and IV fractions are presented. This family of fractions is extended to a wider class of designs formed as the union of cosets of a nontrivial group of treatment combinations. Results are obtained on the aliasing of the main effects of factors in some of these fractions.

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