Blocking in Compound Dispersion Experiments

Abstract

In quality design, a dispersion experiment attempts to estimate the effects of control factors on the dispersion introduced by error factors—that is, the effect of product design on the stability of the performance of the product as its operating environment changes. In conducting a dispersion experiment, it is important to distinguish the sources of dispersion that one wishes to control from extraneous sources of dispersion, so blocking is often necessary. This is especially true when the quality or utility of a product is appraised subjectively, as in conjoint analysis. Compound designs for dispersion experiments are orthogonal array designs that generalize Taguchi's direct product designs. Compared to direct product designs, compound designs are often stronger for a given size or smaller for a given strength. This article discusses blocked compound dispersion experiments. Providing that blocks form an orthogonal array of strength 1 for the error factors, dispersion within blocks may be pooled to estimate dispersion effects. A family of blocked designs is built using Lin's supersaturated half fractions of Hadamard matrices as the within-block arrays; then, these are completed to form error arrays and then folded to form arrays of the needed strength 3.