A multivariate process quality correlation diagnosis method based on grouping technique

Abstract

Correlation diagnosis in multivariate process quality management is an important and challenging issue. In this paper, a new diagnostic method based on quality component grouping is proposed. Firstly, three theorems describing the properties of the covariance matrix of multivariate process quality are established based on the statistical viewpoint of product quality, to prove the correlation decomposition theorem, which decomposes the correlation of all the quality components into a series of correlations of components pairs, and then by using the factor analysis method, all quality components are grouped in order to maximize the correlations in the same groups and minimize the ones between different groups. Finally, on the basis of correlations between different groups are ignored, T2 control charts of component pairs in the same groups are established to form the diagnostic model. Theoretical analysis and practice prove that for the multivariate process quality whose the correlations between different components vary considerably, the grouping technique enables the size of the correlation diagnostic model to be drastically reduced, thus allowing the proposed method can be used as a generalized theoretical model for the correlation diagnosis.