Fractional Replication for Mixed Series

Abstract

The type of experimental designs to be described in this paper was necessitated by a situation which often occurs in engineering research. In such situations, a considerable number of independent variables are involved, and project engineers are accustomed to presenting their results in the form of large numbers of families of curves obtained by keeping all independent variables constant except one. Since each independent variable (factor) is assigned several values (levels) the number of test points to be obtained becomes large, sometimes forbiddingly so. Virtually all the test saving experimental designs which appear in statistical literature require either that the factors involved are at a convenient number of levels (for example, much has been written on designs in which all factors are at the same number of levels), or that some or all of the two factor initeractions are zero. These conditions rarely obtain in engineering experimentation and hence the standard designs ,cannot be used except in special situations. However, the method known as fractional replication gives promise of alleviating this situation. Using fractional replication, it is possible, under certain conditions, to test only a portion of all the possible combinations of levels of factors; and yet be able to test hypotheses on the existence of all main effects and all two factor interactiolns. What is