Estimates for mean and dispersion effects in unreplicated factorial designs

One important goal of experimentation in quality improvement is to minimize the variability of a product or process around a target mean value. Factors which affect variances as well as factors that affect the mean can be identified using the analysis of mean and dispersion. Box and Meyer (1986b) proposed a method of model identification and maximum likelihood estimation for mean and dispersion effects from unreplicated designs. In this article, we address two problems associated with MLE’s. First, asymptotic variance of MLE's for dispersion effects which can be used to judge the significance of factors can be misleading. A possible explanation is provided; simulation results also indicate that the asymptotic, variance underestimates.