Estimating pure-error from near replicates in design of experiments

In design of experiments, setting exact replicates of factor settings enables estimation of pure-error; a model-independent estimate of experimental error useful in communicating inherent system noise and testing model lack-of-fit. Often in practice, the factor levels for replicates are precisely measured rather than precisely set, resulting in near-replicates. This can result in inflated estimates of pure-error due to uncompensated set-point variation. In this article, we review previous strategies for estimating pure-error from near-replicates and propose a simple alternative. We derive key analytical properties and investigate them via simulation. Finally, we illustrate the new approach with an application.