Dominance index for many-to-many correlation and its applicaions to semiconductor yield analysis

As more and more functionalities are packed into a single product, one-response-at-a-time correlation analysis is no longer sufficient to discover critical factors that result in poor qualities or a low yield. Though methodologies of many-to-many correlation analysis have been proposed in the literature, difficulties arise, especially when there exist multi-collinearity effects among variables, to measure the relative importance of a variable´s contribution in the association between a set of responses and a set of factors. Johnson´s dominance analysis (Johnson 2000) offers a general framework for determination of relative importance of independent variables in linear multiple regression models. In this article, we extend Johnson´s dominance index to many-to-many correlation analysis as a measurement to summarize the association relationship between two sets of variables. Actual semiconductor yield-analysis cases are used to illustrate the method and its effectiveness in analysis of two sets of variables.