Orthogonal array designs satisfy many optimal properties under a specified factorial experiment model. In this paper ``Search designs'' are considered for searching one nonzero interaction under the search linear model for a factorial experiment with factors each at two levels. Balanced arrays and orthogonal arrays are commonly used search designs. ``Search probabilities'' are calculated for the comparison of search designs. These search probabilities depend on an unknown parameter, . Three criteria based on the search probabilities are used for comparing designs. We consider two search designs each with 12 runs for a factorial experiment where the nonzero interaction is either a two- or three-factor interaction. The first design is a balanced array of full strength and the other is Plackett-Burman design. We demonstrate, under all three criteria, that the balanced array is more likely to identify the nonzero interaction than the orthogonal array obtained from the Plackett-Burman design.