Identifying dispersion effects in unreplicated multilevel factorial experiments

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Replication of an experiment is generally considered a necessity in order to distinguish between the real effects of the factors being studied and the random variations that are typically present in the measurements. In many settings, however, experimentation is very expensive and there are many factors that need to be studied. Therefore, experiments may be performed on many combinations of factors without any replication. Unreplicated experiments are often used in studying manufacturing processes, for example, that have many different possible inputs whose levels can be varied. The goal of such processes is to manufacture items with specific properties and as little variability as possible.