Abstract: Numerous models have been proposed for experiments that vary the order in which components are added, or steps are performed. Some models have a linear effect of each component's position in the sequence, and others have added quadratic effects and product terms. Kriging models based on a component's position have also been proposed. Before models based on each component's position were introduced, models based on the relative position of each pair of components were popular. Here, we connect these models and provide lack-of-fit tests to assist with model selection and the interpretability of the parameters. Three examples from the literature illustrate the need for these varied models.

Key words and phrases: Component-position model, experimental design, pairwise order model, sequence effects.