AbstractEngineers utilize screening experiments to find significant main effects of factors for quality improvement. After the analysis of the data resulting from this type of experiment, further investigation into the significance of some two‐factor interactions might be desirable. Repeating an experiment of the same size can be costly and time consuming. A follow‐up experiment with half the number of runs from the initial experiment is a good alternative. In this article, we propose two strategies for selecting additional runs to investigate the significance of two‐way interactions that are important to the experimenter. These strategies are based on the findings from the initial experiment. Two examples are presented to illustrate the application of these strategies. Copyright © 2005 John Wiley & Sons, Ltd.