In modern industrial settings, advanced acquisition systems allow for the collection of data in the form of profiles, that is, as functional relationships linking responses to explanatory variables. In this context, statistical process monitoring (SPM) aims to assess the stability of profiles over time in order to detect unexpected behavior. This review focuses on SPM methods that model profiles as functional data, i.e., smooth functions defined over a continuous domain, and apply functional data analysis (FDA) tools to address limitations of traditional monitoring techniques. A reference framework for monitoring multivariate functional data is first presented. This review then offers a focused survey of several recent FDA-based profile monitoring methods that extend this framework to address common challenges encountered in real-world applications. These include approaches that integrate additional functional covariates to enhance detection power, a robust method designed to accommodate outlying observations, a real-time monitoring technique for partially observed profiles, and two adaptive strategies that target the characteristics of the out-of-control distribution. These methods are all implemented in the R package funcharts, available on CRAN. Finally, a review of additional existing FDA-based profile monitoring methods is also presented, along with suggestions for future research.

翻译：在现代工业环境中，先进的采集系统能够以轮廓数据的形式收集数据，即作为响应变量与解释变量之间函数关系的数据。在此背景下，统计过程监控（SPM）旨在评估轮廓随时间变化的稳定性，以检测异常行为。本文综述了将轮廓建模为函数数据（即定义在连续域上的光滑函数）并应用函数数据分析（FDA）工具以解决传统监控技术局限性的SPM方法。首先提出了监控多元函数数据的参考框架。随后，本文重点综述了若干基于FDA的轮廓监控方法，这些方法扩展了该框架以应对实际应用中常见的挑战。其中包括：整合额外函数协变量以提升检测效能的方法、一种旨在容纳异常观测的鲁棒方法、针对部分观测轮廓的实时监控技术，以及两种针对失控分布特性的自适应策略。这些方法均在CRAN上可用的R包funcharts中实现。最后，本文还综述了其他现有的基于FDA的轮廓监控方法，并提出了未来研究的建议。