Functional regression control chart for monitoring ship CO2 emissions

On modern ships, the quick development in data acquisition technologies is producing data-rich environments where variable measurements are continuously streamed and stored during navigation and thus can be naturally modelled as functional data or profiles. Then, both the CO (Formula presented.) emissions (i.e. the quality characteristic of interest) and the variable profiles that have an impact on them (i.e. the covariates) are called to be explored in the light of the new worldwide and European regulations on the monitoring, reporting and verification of harmful emissions. In this paper, we show an application of the functional regression control chart (FRCC) with the ultimate goal of answering, at the end of each ship voyage, the question: given the value of the covariates, is the observed CO (Formula presented.) emission profile as expected? To this aim, the FRCC focuses on the monitoring of residuals obtained from a multivariate functional linear regression of the CO (Formula presented.) emission profiles on the functional covariates. The applicability of the FRCC is demonstrated through a real-case study of a Ro-Pax ship operating in the Mediterranean Sea. The proposed FRCC is also compared with other alternatives available in the literature and its advantages are discussed over some practical examples.