Robust Multivariate Functional Control Chart

TL;DR

This paper introduces RoMFCC, a robust control chart framework designed for high-dimensional multivariate functional data, effectively handling outliers to improve process monitoring in Industry 4.0 applications.

Contribution

The paper presents a novel robust multivariate functional control chart framework that addresses both casewise and cellwise outliers in high-dimensional data.

Findings

RoMFCC outperforms existing schemes in simulations.

Effective detection of outliers in real automotive welding data.

Robust process monitoring in complex manufacturing environments.

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.