Split-plot Experiments with Unusual Numbers of Subplot Runs

In many experimental situations, it may not be feasible or even possible to run experiments in a completely randomized fashion as usually recommended. Under these circumstances, split-plot experiments in which certain factors are changed less frequently than the others are often used. Most of the literature on split-plot designs is based on 2-level factorials. For those designs, the number of subplots is a power of 2. There may however be some situations where for cost purposes or physical constraints, we may need to have unusual number of subplots such as 3, 5, 6, etc. In this article, we explore this issue and provide some examples based on the Plackett and Burman designs. Also algorithmically constructed D-optimal split-plot designs are compared to those based on Plackett and Burman designs.