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Journal of Thermal Analysis and Calorimetry

, Volume 118, Issue 2, pp 1229–1243 | Cite as

Statistical functional approach for interlaboratory studies with thermal data

  • Salvador NayaEmail author
  • Javier Tarrío-Saavedra
  • Jorge López-Beceiro
  • Mario Francisco-Fernández
  • Miguel Flores
  • Ramón Artiaga
Article

Abstract

A new statistical functional data analysis (FDA) approach to perform interlaboratory tests is proposed and successfully applied to thermogravimetry (TG) and differential scanning calorimetry (DSC). This functional approach prevents the typical losses of information associated to the dimension reduction processes. It allows the location and variability of the thermal curves obtained by the application of a particular test procedure. The intra- and inter-laboratory variability and location have been estimated using a FDA approach as well as the traditional reproducibility and repeatability studies. To evaluate the new approach, 105 TG curves and 90 calorimetric curves were obtained from calcium oxalate monohydrate. The obtained curves correspond to seven simulated laboratories, 15 curves per laboratory. Functional mean and variance were estimated. From a functional point of view, these descriptive statistics consider each datum as a curve or function of infinite dimension. Confidence bands were computed using smooth bootstrap resampling. A laboratory consistency study is performed in a functional context. The functional depth approach based on bootstrap resampling is a useful tool to identify outliers among the laboratories. The new FDA approach permits to identify as outliers the thermal curves obtained with old or wrong calibrations. Functional analysis of variance test based on random projections and the false discovery rate procedure (FDR) provides which laboratories obtain significant different thermal curves. This approach can be applied to perform interlaboratory test programs where the response of the test result is functional, as, for example, DSC and TG tests, without having to assume that data follow a Gaussian distribution.

Keywords

Interlaboratory study Functional data analysis Thermogravimetry Differential scanning calorimetry Laboratory consistency Data depth 

Notes

Acknowledgements

This research has been partially supported by the Spanish Ministry of Science and Innovation. Grant MTM2011-22392 (ERDF included). The authors thank the two referees for very helpful comments and suggestions.

References

  1. 1.
    Tarrío-Saavedra J, Naya S, Francisco-Fernández M, Artiaga R, López-Beceiro J. Application of functional anova to the study of thermal stability of micro-nano silica epoxy composites. Chemometrics Intell Lab Syst. 2011;105:114–24.CrossRefGoogle Scholar
  2. 2.
    Tarrío-Saavedra J, Naya S, Francisco-Fernández M, López-Beceiro J, Artiaga R. Functional nonparametric classification of wood species from thermal data. J Therm Anal Calorim. 2011;104:87–100.CrossRefGoogle Scholar
  3. 3.
    Francisco-Fernández M, Tarrío-Saavedra J, Mallik A, Naya S. A comprehensive classification of wood from thermogravimetric curves. Chemometrics Intell Lab Syst. 2012;118:159–72.CrossRefGoogle Scholar
  4. 4.
    Tarrío-Saavedra J, Naya S, López-Beceiro J, Gracia-Fernández C, Artiaga R. Thermooxidative properties of biodiesels and other biological fuels. In: Montero G, Stoycheva M, editors. Biodiesel. Rijeka: INTECH; 2011. p. 47–62.Google Scholar
  5. 5.
    Practice for conducting and interlaboratory study to determine the precision of a test method. Annual Book of ASTM Standards. West Conshohocken, PA: ASTM International E691; 2004.Google Scholar
  6. 6.
    Accuracy (Trueness and precision) of measurement methods and results - Part 2: Basic method for the determination of repeatability and reproducibility of a standard measurement method. Geneva: ISO. International Standard ISO 5725-4-1994; 1994.Google Scholar
  7. 7.
    Hund E, Massart DL, Smeyers-Verbeke J. Interlaboratory studies in analytical chemistry. Ann Chim Acta. 2000;423:145–65.CrossRefGoogle Scholar
  8. 8.
    Lysiak-Pasttuszak E. Interlaboratory analytical performance studies: a way to estimate measurement uncertainty. Oceanologia. 2004;46(3):427–38.Google Scholar
  9. 9.
    Ramsay JO, Silverman BW. Functional data analysis. New York: Springer-Verlag; 2005.Google Scholar
  10. 10.
    Cuevas A, Febrero M, Fraiman R. On the use of the bootstrap for estimating functions with functional data. Comput Stat Data Anal. 2006;51:1063–74.CrossRefGoogle Scholar
  11. 11.
    Fraiman R, Muniz G. Trimmed means for functional data. Test. 2001;10:419–40.CrossRefGoogle Scholar
  12. 12.
    Cuevas A, Febrero M, Fraiman R. Robust estimation and classification for functional data via projection-based depth notions. Comput Stat. 2007;22:481–96.CrossRefGoogle Scholar
  13. 13.
    Cuevas A, Febrero M, Fraiman R. An anova test for functional data. Comput Stat Data Anal. 2004;47:111–22.CrossRefGoogle Scholar
  14. 14.
    Brumback BA, Rice JA. Smoothing spline models for the analysis of nested and crossed samples of curves. J Amer Stat Assoc. 1998;93:961–94.CrossRefGoogle Scholar
  15. 15.
    Ramsay JO, Silverman BW. Applied functional data analysis. New York: Springer-Verlag; 2002.Google Scholar
  16. 16.
    Ramsay JO, Hooker GS. Functional data analysis with R and Matlab. New York: Springer; 2009.CrossRefGoogle Scholar
  17. 17.
    Fan J, Lin KS. Functional anova models for proportional hazards regression. J Amer Stat Assoc. 1998;93:1007–21.CrossRefGoogle Scholar
  18. 18.
    Shen Q, Faraway JJ. An F test for linear models with functional responses. Stat Sin. 2004;14:1239–57.Google Scholar
  19. 19.
    Cuesta-Albertos JA, Febrero-Bande M. A simple multiway anova for functional data. Test. 2010;19:537–57.CrossRefGoogle Scholar
  20. 20.
    R Development Core Team. R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, 2008. http://www.R-project.org.
  21. 21.
    Febrero-Bande M, de la Fuente OM. Statistical computing in functional data analysis: the R package FDA.usc. J Stat Soft. 2012;51:1–28.Google Scholar
  22. 22.
    Febrero-Bande M, Galeano P, González-Manteiga W. Outlier detection in functional data by depth measures, with application to identify abnormal NOx levels. Environmetrics. 2008;19:331–45.CrossRefGoogle Scholar
  23. 23.
    Brunner E, Dette H, Munk A. Box-type approximations in nonparametric factorial designs. J Am Stat Assoc. 1997;92:1494–502.CrossRefGoogle Scholar
  24. 24.
    Miller RG. Simultaneous statistical inference. New York: Springer-Verlag; 1991.Google Scholar
  25. 25.
    Ferraty F, Vieu P. Nonparametric functional data analysis. Berlin: Springer-Verlag; 2006.Google Scholar
  26. 26.
    Tarrío-Saavedra J, López-Beceiro J, Naya N, Artiaga R. Effect of silica content on thermal stability of fumed silica/epoxy composites. Polym Degr Stab. 2008;93:2133–7.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2014

Authors and Affiliations

  • Salvador Naya
    • 1
    Email author
  • Javier Tarrío-Saavedra
    • 1
  • Jorge López-Beceiro
    • 1
  • Mario Francisco-Fernández
    • 2
  • Miguel Flores
    • 3
  • Ramón Artiaga
    • 1
  1. 1.Escola Politécnica SuperiorUniversidade da CoruñaFerrolSpain
  2. 2.Facultade de InformáticaUniversidade da CoruñaA CoruñaSpain
  3. 3.Escuela de Ciencias Físicas y MatemáticasUniversidad de Las AméricasQuitoEcuador

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