Function‐on‐function regression for assessing production quality in industrial manufacturing

Key responses of manufacturing processes are often represented by spatially or time-ordered data known as functional data. In practice, these are usually treated by extracting one or few representative scalar features from them to be used in the following analysis, with the risk of discarding relevant information available in the whole profile and of drawing only partial conclusions. To avoid that, new and more sophisticated methods can be retrieved from the functional data analysis (FDA) literature. In this work, that represents a contribution in the direction of integrating FDA methods into the manufacturing field, the use of function-on-function linear regression modelling is proposed. The approach is based on a finite-dimensional approximation of the regression coefficient function by means of two sets of basis functions, and two roughness penalties to control the degree of smoothness of the final estimator. The potential of the proposed method is demonstrated by applying it to a real-life case study in powder bed fusion additive manufacturing for metals to predict the mechanical properties of an additively manufactured artefact, given the particle size distribution of the powder used for its production.