When factorial experiments are carried out over a period of time, the response may be subject to time trends. This might happen, for example, with the steady buildup of deposits in a test engine. This article shows how to arrange the runs in a factorial experiment in sequences so that the main effects and, sometimes, the two-factor interactions are uncorrelated with linear or quadratic time trends. This is achieved by using the principle of foldover designs. Trendfree sequences are obtained for both 2 n and 3 n factorials.
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Peter W. M. John (1990) studied this question.