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

Abstract

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.

Functional regression control chart for monitoring ship CO2$_{2}$ emissions

“…In particular, in the FRCC framework, the quality characteristic and the covariates are linked through a multiple functional linear regression model (MFLR), where both the response and the explanatory variables can be described by functional data. Recent examples of MFLR model can be found in Palumbo et al, 10 Centofanti et al 11,12 and Chiou et al 13 The idea of monitoring model residuals arises also in SPC with autocorrelated data, for example, time series. [14][15][16] In this setting, residuals from an autoregressive model are used to recover independence of the observations, because conventional control charts are known not to work well if the quality characteristic exhibits even low levels of correlation over time.…”

“…In particular, in the FRCC framework, the quality characteristic and the covariates are linked through a multiple functional linear regression model (MFLR), where both the response and the explanatory variables can be described by functional data. Recent examples of MFLR model can be found in Palumbo et al, 10 Centofanti et al 11, 12 and Chiou et al 13 . The idea of monitoring model residuals arises also in SPC with autocorrelated data, for example, time series 14–16 .…”