Determining baseline profile by diffusion maps

A major step in statistical process control is to establish the standard pattern of a product. Some quality characteristics are best represented by a profile, a functional relationship between a response variable and one or more explanatory variables, which usually results in high-dimension data handling. Here, we propose a method for Phase I analysis based on diffusion maps and clustering to investigate historical profile data sets to establish a standard profile. Diffusion maps are powerful techniques to represent data and reduce dimensionality while preserving the local geometric structure of the data set, in particular its clusters, hence allowing it to be analysed more thoroughly. It has been used successfully in several different problems. We apply it to real data coming from a wood board production process, highlighting its capabilities in analyzing sets of profiles for baseline profile estimation. We are able to identify two stable production modes, i.e., in control, and several outliers. This is possible due to the enhancement of the geometric understanding of the profile data set allowed by diffusion maps. For validation purposes and to gain insight in its properties, we present a new explicit analytic expression for the diffusion maps of an idealised data set. Furthermore, we apply the method to artificially generated data sets based on a given family of nonlinear profiles. Our results are compared with those in the literature, showing that the proposed method has good performance and, moreover, gives a better insight in the similarities of a real profile data set.