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.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.