Functional Regression Control Chart

The modern development of data acquisition technologies in many industrial processes is facilitating the collection of quality characteristics that are apt to be modeled as functions, which are usually referred to as profiles. At the same time, measurements of concurrent variables, which are related to the quality characteristic profiles, are often available in a functional form as well, and usually referred to as covariates. To adjust the monitoring of the quality characteristic profiles by the effect of this additional information, a new functional control chart is elaborated on the residuals obtained from a function-on-function linear regression of the quality characteristic profile on the functional covariates. By means of a Monte Carlo simulation study, the proposed control chart is compared with other control charts already appeared in the literature and some remarks are given on its use in presence of covariate mean shifts. Furthermore, a real-case study in the shipping industry is presented with the purpose of monitoring ship fuel consumption and thus, CO₂ emissions from a Ro-Pax ship, with particular regard to detecting their reduction after a specific energy efficiency initiative.