Methods for assessing multivariate interactions in a manufacturing system

Abstract

Statisticians use the term interaction for situations wherein the effect of one variable depends upon another variable [McNeil, Francis, McNeil, 1975]. A deep knowledge about interdependencies and interactions among elements within a domain is conducive to devising action plans towards a desired situation. It allows for product or systems optimization, preventing pitfalls and diagnosing malfunctions. As part of a project to develop a knowledge based system for supporting research activities in the field of polymeric adhesives, we compared different methods of assessing interactions. Here, we employed general liner models as a classical approach, characteristic angles, self-organizing maps (SOM) and interactive visual feature extraction methods (IVFEM) as alternative techniques. The latter is based on a data projection method, where attributes are mapped to areas that can then be selected interactively. In this manner, we can describe interaction in terms of shared attribute regions in proportion to combined area. As a quantization method, we initialize SOMs with characteristic angles to illustrate partial interactions. Characteristic angles based on multivariate analysis of the angles between eigenvectors can be utilized to describe partial interactions associated with an explained variability.