A Comparison Study of Control Charts for Statistical Monitoring of Functional Data
Résumé
Quality of products and processes is more and more often related to functional data, which refer to information summarized in form of profiles. Recent literature 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 up to now. This paper aims at filling this lack by comparing three representative profile monitoring approaches in different productive scenarios. The performance comparison will allow one to select a specific approach in a given situation. The competitor approaches are chosen for representing different levels of complexity, as well as different types of modelling approach. 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 as representative of the industrial practice. At a higher complexity level, approaches based on combining a parametric model of functional data to 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 reference case study in manufacturing is used throughout the paper, namely, profiles measured on machined items subjected to geometrical specification (roundness).
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