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A comparison study of control charts for statistical monitoring of functional data

机译：功能图统计监视控制图的比较研究

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摘要

The quality of products and processes is more and more often becoming related to functional data, which refer to information summarised in the form of profiles. The recent literature has pointed out that traditional control charting methods cannot be directly applied in these cases and new approaches for profile monitoring are required. While many different profile monitoring approaches have been proposed in the scientific literature, few comparison studies are available. This paper aims at filling this gap by comparing three representative profile monitoring approaches in different production scenarios. The performance comparison will allow us to select a specific approach in a given situation. The competitor approaches are chosen to represent different levels of complexity, as well as different types of modelling approaches. In particular, at a lower level of complexity, the 'location control chart' (where the upper and lower control limits are ± K standard deviations from the sample mean at each profile location) is considered to be representative of industrial practice. At a higher complexity level, approaches based on combining a parametric model of functional data with multivariate and univariate control charting are considered. Within this second class, we analyse two different approaches. The first is based on regression and the second focuses on using principal component analysis for modelling functional data. A manufacturing reference case study is used throughout the paper, namely profiles measured on machined items subject to geometrical specification (roundness).
机译：产品和过程的质量越来越与功能数据相关，功能数据是指以概要文件形式概括的信息。最近的文献指出，传统的控制制图方法不能直接应用于这些情况，需要新的轮廓监测方法。尽管在科学文献中已经提出了许多不同的轮廓监测方法，但是很少有比较研究可用。本文旨在通过比较不同生产场景中的三种代表性轮廓监测方法来填补这一空白。性能比较将使我们能够在给定情况下选择特定的方法。选择竞争对手的方法来代表不同级别的复杂性以及不同类型的建模方法。特别是，在较低的复杂性水平下，“位置控制图”（其中控制上限和下限为每个轮廓位置处与样本平均值的±K标准偏差）代表了工业实践。在更高的复杂性级别上，考虑了基于将功能数据的参数模型与多变量和单变量控制图相结合的方法。在第二堂课中，我们分析了两种不同的方法。第一个基于回归，第二个专注于使用主成分分析对功能数据进行建模。整篇论文都使用了制造参考案例研究，即在受几何规格（圆度）约束的机加工项目上测量的轮廓。

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