Some Comments on Compositional Analysis in Management and Production Engineering

• Autorzy: Marina Vives-Mestres , Josep A. Martín-Fernández
• Języki publikacji: EN

Abstrakty

EN

This paper introduces the most basic concepts of the compositional analysis of data with a simple but real example form the Management and Production Engineering (MPE) field. Compositional Data (CoDa) are vectors of positive elements that represent parts of a whole and are widely found in MPE, i.e. production times, resource composition, percentage utilization of work stands, waste components. . . The need for an analysis based on ratios of components (or better log-ratios of components) is illustrated step by step, and findings are compared to the corresponding standard methods applied to raw compositions. The paper also exposes the principles of CoDa analysis and presents two basic descriptive tools suitable for CoDa: the clr-biplot and the CoDa dendrogram. The example is a time series, from 1994 to 2013, of motor vehicle production in 8 countries and regions. (original abstract)

Słowa kluczowe

EN

Statistical analysis; Management; Production engineering

PL

Analiza statystyczna; Zarządzanie; Inżynieria produkcji

• Czasopismo: Management and Production Engineering Review
• Rocznik: 2015
• Tom: 6
• Numer: nr 2
• Strony: 63--72

Twórcy

autor

Marina Vives-Mestres

• University of Girona, Spain

autor

Josep A. Martín-Fernández

• University of Girona, Spain

Bibliografia

• [1] Aitchison J., The Statistical Analysis of Compositional Data, Monographs on Statistics and Applied Probability. Chapman and Hall Ltd (reprinted 2003 with additional material by The Blackburn Press), London (UK), 1986.
• [2] Hron K., Filzmoser P., Templ M. [Eds.], Proceedings of the 5th International Workshop on Compositional Data Analysis, Codawork'13 June 3-7, Vorau, Austria, 2013, ISBN: 978-3-200-03103-6.
• [3] Pawlowsky- Glahn V., Buccianti A. [Eds.], Compositional Data Analysis: Theory and Applications, John Wiley & Sons, Chichester (UK), 2011.
• [4] Mateu-Figueras G., Pawlowsky-Glahn V., Egozcue J.J., The principle of working on coordinates and compositional data analysis, [in:] Compositional Data Analysis: Theory and Applications, Pawlowsky-Glahn V., Buccianti A. [Eds.], Wiley & Sons (UK), 2011.
• [5] Vives-Mestres M., Daunis-i-Estadella J., Martin-Fernandez J.A., Individual T2 control chart for Compositional Data, Journal of Quality Technology, 46 (2), 127-139, April 2014.
• [6] Vives-Mestres M., Daunis-i-Estadella J., Martin-Fernandez J.A., Out-of-Control signals in 3-part Compositional T2 control chart, Quality and Reliability Engineering International, 30 (3), 337- 346, April 2014.
• [7] Vives-Mestres M., Daunis-i-Estadella J., Martin-Fernandez J.A., Signal interpretation in Hotelling's T2 control chart for Compositional Data, unpublished.
• [8] R development core team 2013. R: A language and environment for statistical computing: Vienna, http://www.r-project.org.
• [9] Comas-Cufi M., S. Thió- Henestrosa, CoDaPack 2.0: a stand-alone, multi-platform compositional software, [in:] Egozcue J.J., Tolosana- Delgado R., Ortego M.I. [Eds.], CoDaWork'11: 4th International Workshop on Compositional Data Analysis, Sant Feliu de Guixols, 2011.
• [10] Grunwald G.K., Raftery A.E., Guttorp P., Time Series of Continuous Proportions. Journal of the Royal Statistical Society, Series B (Methodological), 55 (1), 103-116, 1993.
• [11] Pearson K., Mathematical contributions to the theory of evolution. On a form of spurious correlation which may arise when indices are used in the measurement of organs, Proceedings of the Royal Society of London LX, 489-502, 1897.
• [12] Chacón J.E., Mateu-Figueras G., Martin-Fernandez J.A., Gaussian kernels for density estimation with compositional data, Computer&Geosciences, 37, 702-711, 2011.
• [13] Palarea-Albaladejo J., Martin-Fernandez J.A., Soto J.A., Dealing with Distances and Transformations for Fuzzy C-Means Clustering of Compositional Data, Journal of Classification, 29 (2), 144-169, 2012.
• [14] Pawlowsky-Glahn V., Egozcue J.J., Geometric approach to statistical analysis on the simplex, Stochastic Environmental Research and Risk Assessment (SERRA), 15 (5), 384-398, 2001.
• [15] Egozcue J.J., Pawlowsky-Glahn V., Mateu-Figueras G., Barceló-Vidal C., Isometric logratio transformations for compositional data analysis, Mathematical Geology, 35 (3), 279-300, 2003.
• [16] Thió-Henestrosa S., Egozcue J.J., Pawlowsky-Glahn V., Kovacs L.O., G. Kovacs, Balance-dendrogram a new routine of CoDaPack, Computer and Geo- sciences, 34 (12), 1682-1696, 2008.
• [17] Pawlowsky-Glahn V., Egozcue J.J., Exploring Compositional Data with the Coda-Dendrogram, Austrian Journal of Statistics, (1-2), 103-113, 2011.
• [18] Palarea-Albaladejo J., Martin-Fernandez J.A., zCompositions - R package for multivariate imputation of nondetects and zeros in compositional data sets, Chemometrics and Intelligent Laboratory Systems, 143, 85-96, 2015.
• [19] Greenacre M., Compositional data and correspondence analysis, [in:] Compositional Data Analysis: Theory and Applications, Pawlowsky-Glahn V., Buccianti A. [Eds.], Wiley & Sons (UK), 2011.

Identyfikatory

DOI

10.1515/mper-2015-0018