Robust Multivariate Functional Control Chart

Abstract

In modern Industry 4.0 applications, a huge amount of data is acquired during manufacturing processes that are often contaminated with anomalous observations in the form of both casewise and cellwise outliers. These can seriously reduce the performance of control charting procedures, especially in complex and high-dimensional settings. To mitigate this issue in the context of profile monitoring, we propose a new framework, referred to as robust multivariate functional control chart (RoMFCC), that is able to monitor multivariate functional data while being robust to both functional casewise and cellwise outliers. The RoMFCC relies on four main elements: (I) a functional univariate filter to identify functional cellwise outliers to be replaced by missing components; (II) a robust multivariate functional data imputation method of missing values; (III) a casewise robust dimensionality reduction; (IV) a monitoring strategy for the multivariate functional quality characteristic. An extensive Monte Carlo simulation study is performed to compare the RoMFCC with competing monitoring schemes already appeared in the literature. Finally, a motivating real-case study is presented where the proposed framework is used to monitor a resistance spot welding process in the automotive industry.

References in corpus (6)

• Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains
• Propagation of outliers in multivariate data
• Detecting deviating data cells
• Robust estimation of precision matrices under cellwise contamination
• Robust Functional ANOVA with Application to Additive Manufacturing
• Real-time Monitoring of Functional Data

Cited by in corpus (2)

• Covariate-Adjusted Functional Data Analysis for Structural Health Monitoring
• Robust Principal Components by Casewise and Cellwise Weighting