Profile control charts based on nonparametric $L$-1 regression methods

TL;DR

This paper introduces a new nonparametric $L$-1 regression-based control chart method for monitoring functional profiles in quality control, capturing shape distortions and deviations more effectively than traditional univariate approaches.

Contribution

It develops a novel $L$-1 location-scale model for profile monitoring, incorporating shape and deviation metrics, advancing the analysis of complex functional data.

Findings

Applied to vertical density profile data with insightful results

Effectively detects shape distortions and deviations in profiles

Enhances profile monitoring beyond traditional methods

Abstract

Classical statistical process control often relies on univariate characteristics. In many contemporary applications, however, the quality of products must be characterized by some functional relation between a response variable and its explanatory variables. Monitoring such functional profiles has been a rapidly growing field due to increasing demands. This paper develops a novel nonparametric $L$-1 location-scale model to screen the shapes of profiles. The model is built on three basic elements: location shifts, local shape distortions, and overall shape deviations, which are quantified by three individual metrics. The proposed approach is applied to the previously analyzed vertical density profile data, leading to some interesting insights.