Simultaneous identification of premodeled and unmodeled variation patterns

For purposes of identifying root causes of variation in multivariate manufacturing data, many studies employ a linear structured model. One paradigm involves modeling off-line a set of variation patterns and then attempting to detect the presence or absence of those specific premodeled patterns in a sample of on-line data. In another paradigm, which requires no premodeling, the objective is to discover the nature of any variation patterns that are present, based only on the on-line data sample. In this paper, we present a method that combines the two paradigms and mitigates some of the shortcomings of each. Instead of exhaustively premodeling all potential variation patterns, which is infeasible for many processes, one premodels only the patterns for which modeling is relatively easy. The characteristics of any unmodeled patterns that also happen to be present in the on-line data are discovered automatically, and they are treated in such a manner that their presence does not adversely affect the detection of the premodeled patterns. We illustrate the approach with an example from autobody assembly.