Niu Qing, Cheng Shujie, Qiu Zeyang
Department of Product Design, Lanzhou Jiaotong University, Lanzhou, Gansu, People's Republic of China.
Sci Rep. 2024 Jun 8;14(1):13212. doi: 10.1038/s41598-024-61954-y.
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, T 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.
多变量过程质量管理中的相关性诊断是一个重要且具有挑战性的问题。本文提出了一种基于质量成分分组的新诊断方法。首先，基于产品质量的统计观点建立了描述多变量过程质量协方差矩阵性质的三个定理，以证明相关性分解定理，该定理将所有质量成分的相关性分解为一系列成分对的相关性，然后通过因子分析方法，对所有质量成分进行分组，以使同一组内的相关性最大化，不同组之间的相关性最小化。最后，在忽略不同组之间相关性的基础上，建立同一组内成分对的T控制图以形成诊断模型。理论分析和实践证明，对于不同成分之间相关性差异较大的多变量过程质量，分组技术能够大幅减小相关性诊断模型的规模，从而使所提出的方法可作为相关性诊断的广义理论模型。
