Optimality and construction of search designs in factorial experiments

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Consider factorial experiments with m factors each at two levels. It is assumed that the general mean and main effects are completely unknown. However the effects of interactions are partially unknown in the sense. At most k interactions are nonzero and the remaining are zero, where k is a quite small integer. Then it is not known which are the nonzero effects. Such a model is called a search linear model. The problem is to search the k nonzero interactions and to estimate them along the general mean and main effects using observations. A experimental design which makes possible to solve the problem is called a search design of order k.□ Consider for two cases; (i) the k effects searched are among the two-factor interactions, and (ii) they are among the two-factor and three-factor interactions. In this researches, search designs of order k = 1, 2 were constructed for the cases (i) and (ii), and search designs of order k = 3 were constructed for the case (ii). Also we define a searching power how large the precision is that a search design could search the k nonzero effects. Using searching powers, search designs were compared.