Simultaneous estimation of location and dispersion in two-level fractional factorial designs

Abstract

The reduction of variation is one of the obvious goals in quality improvement. The identification of factors aff ecting the dispersion is a step towards this goal. In this paper, the problem of estimating location effects and dispersion eff ects simultaneously in unreplicated factorial experiments is considered. By making a one-to-one transformation of the response variables, the study of the quadratic functions becomes clearer. The transformation also gives a natural motivation to the model of the variances of the original variables. The covariances of the transformed responses appear as parameters in the variances of the original variables. Results of Hadamard products are used for deriving these covariances. The method of estimating dispersion effects is shown in two illustrations. In a 24 factorial design, the essential covariance matrix of the transformed variables is also presented. The method is also illustrated in a 25-1 fractional design with a model which is saturated in this context.