Designing Experiments for Causal Networks

摘要

Causal networks are directed graphs representing cause-effect relationships and are multiple-response generalizations of Ishikawa's cause-effect diagrams. Emphasizing tolerance design applications, this article describes an algorithm for designing suitable experiments when the factors and responses are organized as a causal network. The causal network is transformed into a so-called causal map, which represents all factors and responses as points in a common D-dimensional metric space. The design approach is algorithmic, optimizing the entropy criterion due to Wynn. This criterion is applied to maximize dispersion among the multiple responses, using a distance-in-space coefficients model. A key constraint is for the blocks to he self-contained; this implies that each block can he analyzed without reference to other blocks. This is to be complemented by a unified, all-block analysis. The resulting designs are evaluated for efficiency, response dispersion, and resolution V column rank. Particular attention is given to skewing each block by shifting one or a few factors off-center.