Identifying dispersion effects in unreplicated multilevel factorial experiments

为了区分正在研究的因素的实际影响和测量中通常存在的随机变化，通常认为有必要进行实验。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许多因素组合进行实验。例如，在研究制造过程中经常使用未重复的实验。有许多不同的可能的输入，其水平可以不同。这些过程的目标是制造具有特定性质和尽可能少的变异性的物品。已经开发出专门的统计分析方法来确定哪些因素或交互作用可能影响被研究过程的平均产量。已经开发出方法来研究哪些因素或交互作用影响过程的可变性，这被称为分散效应。这项工作将产生更好、更可靠的方法来研究分散效应，因此，与目前的分析方法相比，从非重复实验中可以获得更多的信息。传统上使用非重复实验的工业和其他实验者将能够更清楚地识别哪些因素可能影响其过程的可变性，并将能够更好地设计或以其他方式开发程序，在最大限度地提高产量的同时将变异性降至最低。这项工作的影响可能非常广泛，并在广泛的行业和其他环境中带来巨大的效率提升。

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.Specialised statistical analysis methods have been developed to identify which factors or interactions may affect the average output of a process being studied.  Fewer, less reliable, methods have been developed for studying which factors or interactions affect the variability of the process, which are called "dispersion effects".  This work will result in better, more reliable methods for studying dispersion effects, thereby permitting substantially more information to be gained from unreplicated experiments than is possible with the current methods of analysis.  Industries and other experimenters that have traditionally used unreplicated experiments will be able to identify more clearly which factors may be affecting the variability of their processes and will be better able to engineer or otherwise develop procedures that can maximize output while minimizing variability.  The impact of this work could be very broad-reaching and result in tremendous gains in efficiency in a wide range of industries and in other settings.