Gestão & Produção
Gestão & Produção
Seção Temática: Monitoramento e Controle Estatístico de Processos

A functional data analysis approach for the monitoring of ship CO2 emissions

Christian Capezza; Fabio Centofanti; Antonio Lepore; Biagio Palumbo

Downloads: 0
Views: 47


Abstract: Sensing networks provide nowadays massive amounts of data that in many applications provide information about curves, surfaces and vary over a continuum, usually time, and thus, can be suitably modelled as functional data. Their proper modelling by means of functional data analysis approaches naturally addresses new challenges also arising in the statistical process monitoring (SPM). Motivated by an industrial application, the objective of the present paper is to provide the reader with a very transparent set of steps for the SPM of functional data in real-world case studies: i) identifying a finite dimensional model for the functional data, based on functional principal component analysis; ii) estimating the unknown parameters; iii) designing control charts on the estimated parameters, in a nonparametric framework. The proposed SPM procedure is applied to a real-case study from the maritime field in monitoring CO2 emissions from real navigation data of a roll-on/roll-off passenger cruise ship, i.e., a ship designed to carry both passengers and wheeled vehicles that are driven on and off the ship on their own wheels. We show different scenarios highlighting clear and interpretable indications that can be extracted from the data set and support the detection of anomalous voyages.


Profile monitoring, Functional principal component analysis, CO2 emissions, Control charts, Statistical process monitoring


Bersimis, S., Sgora, A., & Psarakis, S. (2018). The application of multivariate statistical process monitoring in non-industrial processes. Quality Technology & Quantitative Management, 15(4), 526-549.

Bocchetti, D., Lepore, A., Palumbo, B., & Vitiello, L. (2015). A statistical approach to ship fuel consumption monitoring. Journal of Ship Research, 59(3), 162-171.

Bosq, D. (2012). Linear processes in function spaces: theory and applications (Lecture Notes in Statistics). New York: Springer.

Capezza, C., Centofanti, F., Lepore, A., Menafoglio, A., Palumbo, B., & Vantini, S. (2021). Funcharts: functional control charts. R package version 1.0.0. Vienna: R Foundation for Statistical Computing. Retrieved in 2020, September 28, from

Capezza, C., Coleman, S., Lepore, A., Palumbo, B., & Vitiello, L. (2019). Ship fuel consumption monitoring and fault detection via partial least squares and control charts of navigation data. Transportation Research Part D, Transport and Environment, 67, 375-387.

Capezza, C., Lepore, A., Menafoglio, A., Palumbo, B., & Vantini, S. (2020). Control charts for monitoring ship operating conditions and CO emissions based on scalar-on-function regression. Applied Stochastic Models in Business and Industry, 36(3), 477-500.

Cardot, H., Ferraty, F., & Sarda, P. (2003). Spline estimators for the functional linear model. Statistica Sinica, 13, 571-591.

Centofanti, F., Lepore, A., Menafoglio, A., Palumbo, B., & Vantini, S. (2020). Functional regression control chart. Technometrics, 1-14.

Colosimo, B. M., & Pacella, M. (2007). On the use of principal component analysis to identify systematic patterns in roundness profiles. Quality and Reliability Engineering International, 23(6), 707-725.

Colosimo, B. M., & Pacella, M. (2010). A comparison study of control charts for statistical monitoring of functional data. International Journal of Production Research, 48(6), 1575-1601.

De Boor, C., De Boor, C., Mathématicien, E.-U., De Boor, C., & De Boor, C. (1978). A practical guide to splines (Vol. 27). New York: Springer-Verlag.

Erto, P., Lepore, A., Palumbo, B., & Vitiello, L. (2015). A procedure for predicting and controlling the ship fuel consumption: its implementation and test. Quality and Reliability Engineering International, 31(7), 1177-1184.

Eubank, R. L. (1999). Nonparametric regression and spline smoothing. Boca Raton: CRC Press.

Grasso, M., Colosimo, B. M., & Tsung, F. (2017). A phase I multi-modelling approach for profile monitoring of signal data. International Journal of Production Research, 55(15), 4354-4377.

Grasso, M., Menafoglio, A., Colosimo, B. M., & Secchi, P. (2016). Using curve-registration information for profile monitoring. Journal of Quality Technology, 48(2), 99-127.

Green, P. J., & Silverman, B. W. (1993). Nonparametric regression and generalized linear models: a roughness penalty approach. Boca Raton: Chapman & Hall/CRC.

Gu, C. (2013). Smoothing spline ANOVA models (Vol. 297). New York: Springer Science & Business Media.

Horváth, L., & Kokoszka, P. (2012). Inference for functional data with applications. New York: Springer Science & Business Media.

Hsing, T., & Eubank, R. (2015). Theoretical foundations of functional data analysis, with an introduction to linear operators. West Sussex: John Wiley & Sons.

Jin, J., & Shi, J. (1999). Feature-preserving data compression of stamping tonnage information using wavelets. Technometrics, 41(4), 327-339.

Jolliffe, I. (2011). Principal component analysis. Cham: Springer.

Kokoszka, P., & Reimherr, M. (2017). Introduction to functional data analysis. Boca Raton: CRC Press.

Lehmann, E. L., & Romano, J. P. (2006). Testing statistical hypotheses. New York: Springer Science & Business Media.

Lepore, A., Palumbo, B., & Capezza, C. (2019). Orthogonal LS-PLS approach to ship fuel-speed curves for supporting decisions based on operational data. Quality Engineering, 31(3), 386-400.

Lowry, C. A., & Montgomery, D. C. (1995). A review of multivariate control charts. IIE Transactions, 27(6), 800-810.

Mandel, B. (1969). The regression control chart. Journal of Quality Technology, 1(1), 1-9.

Menafoglio, A., Grasso, M., Secchi, P., & Colosimo, B. M. (2018). Profile monitoring of probability density functions via simplicial functional PCA with application to image data. Technometrics, 60(4), 497-510.

Montgomery, D. C. (2007). Introduction to statistical quality control. Hoboken: John Wiley & Sons.

Nomikos, P., & MacGregor, J. F. (1995). Multivariate SPC charts for monitoring batch processes. Technometrics, 37(1), 41-59.

Noorossana, R., Saghaei, A., & Amiri, A. (2012). Statistical analysis of profile monitoring. Hoboken: John Wiley & Sons.

Pini, A., & Vantini, S. (2017). Interval-wise testing for functional data. Journal of Nonparametric Statistics, 29(2), 407-424.

Pini, A., Vantini, S., Colosimo, B. M., & Grasso, M. (2018). Domain-selective functional analysis of variance for supervised statistical profile monitoring of signal data. Journal of the Royal Statistical Society. Series C, Applied Statistics, 67(1), 55-81.

R Core Team. (2020). R: a language and environment for statistical computing. Vienna: R Foundation for Statistical Computing.

Ramsay, J. O., & Silverman, B. W. (2005). Functional data analysis. New York: Wiley.

Shang, H. L. (2014). A survey of functional principal component analysis. AStA. Advances in Statistical Analysis, 98(2), 121-142.

Wahba, G. (1990). Spline models for observational data (Vol. 59). Phyladelphia: Society for Industrial and Applied Mathematics.

Woodall, W. H., Spitzner, D. J., Montgomery, D. C., & Gupta, S. (2004). Using control charts to monitor process and product quality profiles. Journal of Quality Technology, 36(3), 309-320.

6126515aa953957afa0c4782 gp Articles

Gest. Prod.

Share this page
Page Sections