Using independent component analysis to monitor 2-D geometric specifications

摘要

Functional data and profiles are characterized by complex relationships between a response and several predictor variables. Fortunately, statistical process control methods provide a solid ground for monitoring the stability of these relationships over time. This study focuses on the monitoring of 2-dimensional geometric specifications. Although the existing approaches deploy regression models with spatial autoregressive error terms combined with control charts to monitor the parameters, they are designed based on some idealistic assumptions that can be easily violated in practice. In this paper, the independent component analysis (ICA) is used in combination with a statistical process control method as an alternative scheme for phase II monitoring of geometric profiles when non-normality of the error term is present. The performance of this method is evaluated and compared with a regression- and PCA-based approach through simulation of the average run length criterion. The results reveal that the proposed ICA-based approach is robust against non-normality in the in-control analysis, and its out-of-control performance is on par with that of the PCA-based method in case of normal and near-normal error terms.