Testing dispersion effects from general unreplicated fractional factorial designs

Continuous improvement of the quality of industrial products is an essential factor in modern-day manufacturing. The investigation of those factors that affect process mean and process dispersion (standard deviation) is an important step in such improvements. Most often, experiments are executed for such investigations. To detect mean factors, I use the usual analysis of variance on the experimental data. However, there is no unified method to identify dispersion factors. In recent years several methods have been proposed for identifying such factors with two levels. Multilevel factors, especially three-level factors, are common in industrial experiments, but we lack methods for identifying dispersion effects in multilevel factors. In this paper, I develop a method for identifying dispersion effects from general fractional factorial experiments. This method consists of two stages. The first stage involves the identification of mean factors using the performance characteristic as the response. The second stage involves the computation of a dispersion measure and the identification of dispersion factors using the dispersion measure as the response. The sequence for identifying dispersion factors is first to test the significance of the total dispersion effect of a factor, then to test the dispersion contrasts of interest, which is a method similar to the typical post hoc testing procedure in the ANOVA analysis. This familiar approach should be appealing to practitioners.