Identifying dispersion effects in unreplicated multilevel factorial experiments

重复实验通常被认为是必要的，以便区分正在研究的因素的实际影响和通常存在于测量中的随机变化。然而，在许多情况下，实验是非常昂贵的，并且有许多因素需要研究。因此，可以在没有任何重复的情况下对多种因素组合进行实验。未重复的实验经常用于研究制造过程，例如，有许多不同的可能输入，其水平可能会有所不同。这种工艺的目标是制造具有特定特性和尽可能少的可变性的产品。

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.