In designing an experiment for modelling both mean and dispersion, it is advisable to have estimates of dispersion based on pure replicates. To a large extent the impetus for studying the extended class of models derives from the surge of interest in industrial quality-improvement experiments in which both the mean response and the signal-to-noise ratio are of substantive interest. For economy of effort, fractional factorial and related experimental designs are often used for this purpose. The aim very often is to select that combination of factor levels that keeps the mean at a pre-determined ‘ideal’ value, while at the same time keeping the variability in the product at a minimum. Omission of an interaction between two factors in the linear predictor for the mean will result in the inflation of supposedly null contrasts used to model the dispersion. The original analysis by Pignatiello and Ramberg uses a linear model for the logarithms of the within-replicate sample variances.