Trend-free designs in blocked factorial experiments

Appropriate run orders can make all estimable effects free of some trends in blocked fractional factorial experiments. We need to design blocked experiments with effects free of trends in blocks. The generalized foldover scheme given by Coster (1993) can be used to obtain such designs. In this article, we propose an easy and better approach to deal with this issue when the same trends appear in blocks. We investigate block trend property of columns in the orthogonal plans in sk runs for assigning factors to obtain block-trend free designs in a trend-free order. We illustrate our approach with three examples.