Control Charts for functional data: a comparison study

In many industrial applications quality of products or processes is more and more often related to functional data, which refer to information summarized in form of curves or functions. Examples of functional data are the vector of points measured on a machined profile which is subject to geometrical specification or the high- dimensional data vector related to process signals sampled at high frequency. In order to deal with functional data monitoring, different approaches can be considered. A first simple approach, consists in designing a “location control chart”, where the upper and lower control limits are three standard deviations from the sample mean at each location. A different approach proposed in the recent literature on profile monitoring, consists in combining approach for functional data analysis (as the Principal Component Analysis - PCA) to multivariate control charting. The main objective of this paper is to compare the performances of these two approaches, namely, the “location control chart” and the “PCA-based control charts”. Because of its inner simplicity, the location control chart is the common method adopted in industrial practice for monitoring signals and curves. However, this paper shows that the PCA-based approach outperforms this simple method both in the ability to obtain a predefined false alarm rate as well as in the promptness to detect unusual patterns in the functional data. Throughout the paper, a real case study related to roundness profiles of mechanical components is used as reference