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Prediction of precision from signal and noise measurement in liquid chromatography: Mathematical relationship between integration domain and precision

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Summary

The precision of integration over noisy instrumental output for quantitative analysis is studied. A probability theory is developed to predict the relative standard deviation (RSD) of integration results over an integration domain from one-point integation (peak height measurement) to entire area integration in HPLC. Common integration modes of horizontal zero line and oblique zero line are taken into account, but no peak overlap is assumed. The question of the analytical superiority of peak height measurement or integration for quantitation is answered. In the HPLC apparatus used, the minimum RSD of measurements is found in the integration domain of ca. ±0.5 σ for analytes [peaks are approximated by the Gaussian signal of width, σ (standard deviation)]. The RSD of integration measurements is also shown to depend on the stochastic properties of back-ground noise (uncorrelated noise and correlated 1/f type noise). The theoretical conclusion is verified by Monte Carlo simulation and HPLC experiments for some aromatic compounds.

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References

  1. Y. Hayashi, R. Matsuda, Chromatographia41, 66 (1995).

    Google Scholar 

  2. A. W. Westerberg, Anal. Chem.41, 1770 (1969).

    Google Scholar 

  3. L. R. Snyder, J. Chrom. Sci.10, 200 (1972).

    Google Scholar 

  4. J. P. Foley, J. Chromatogr.384, 301 (1987).

    Google Scholar 

  5. A. N. Papas, M. F. Delaney, Anal. Chem.59, 54A (1987).

    Google Scholar 

  6. N. Dyson, Chromatographic integration methods, Cambridge: Royal Society of Chemistry, 1990.

    Google Scholar 

  7. E. Grushka, I. Zamir, Chemical Analysis, 1989, Chapter 13.

  8. J. F. K. Huber, J. A. R. J. Hulsman, C. A. M. Meijers, J. Chromatogr.62, 79 (1971).

    Google Scholar 

  9. H. Barth, E. Dallmeier, G. Courtois, H. E. Keller, B. L. Karger, J. Chromatogr.83, 289 (1973).

    Google Scholar 

  10. S. R. Bakalyar, R. A. Henry, J. Chromatogr.126, 327 (1976).

    Google Scholar 

  11. R. P. W. Scott, C. E. Reese, J. Chromatogr.138, 283 (1977).

    Google Scholar 

  12. I. Halász, P. Vogtel, J. Chromatogr.142, 241 (1977).

    Google Scholar 

  13. L. R. Snyder, S. van der Wal, Anal. Chem.53, 877 (1981).

    Google Scholar 

  14. Y. Hayashi, R. Matsuda, Chemom. Intell. Lab Syst.18, 1 (1993).

    Google Scholar 

  15. Y. Hayashi, R. Matsuda, Advances in Chromatography1994. Chapter 7.

  16. Y. Hayashi, R. Matsuda, Anal. Sci.10, 553 (1994).

    Google Scholar 

  17. R. B. Poe, S. C. Rutan, Anal. Chim. Acta283, 845 (1993).

    Google Scholar 

  18. R. E. Synovec, E. S. Yeung, Anal. Chem.57, 2162 (1985).

    Google Scholar 

  19. T. Hirschfeld, Appl. Spectrosc.30, 67 (1976).

    Google Scholar 

  20. E. H. Piepmeier, Anal. Chem.48, 1296 (1976).

    Google Scholar 

  21. Y. Hayashi, R. Matsuda, Anal. Chem.66, 2874 (1994).

    Google Scholar 

  22. H. C. Smit, H. L. Walg, Chromatographia8, 311 (1975).

    Google Scholar 

  23. A. Bezegh, J. Janata, Anal. Chem.59, 494A (1987).

    Google Scholar 

  24. I. G. Giles, M. G. Gore, Anal. Chim. Acta151, 123 (1983).

    Google Scholar 

  25. R. P. Singhal, D. B. Smoll, J. Liquid Chromatogr.9, 2719 (1986).

    Google Scholar 

  26. J. Olivo, P. Cardot, I. Ignatiadis, C. Vidal-Madjar, J. Chromatogr.395, 383 (1987).

    Google Scholar 

  27. P. J. P. Cardot, P. Trolliard, S. Tembely, J. Pharm. Biomed. Anal.8, 755 (1990).

    Google Scholar 

  28. M. O. Koskinen, L. K. Koskinen, J. Liquid Chromatogr.16, 3171 (1993).

    Google Scholar 

  29. C. N. Renn, R. E. Synovec, Anal. Chem.60, 1829 (1988).

    Google Scholar 

  30. A. W. Moore, Jr., J. W. Jorgenson, Anal. Chem.65, 188 (1993).

    Google Scholar 

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Second Part of series cited as Ref. [1].

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Hayashi, Y., Matsuda, R. Prediction of precision from signal and noise measurement in liquid chromatography: Mathematical relationship between integration domain and precision. Chromatographia 41, 75–83 (1995). https://doi.org/10.1007/BF02274198

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  • DOI: https://doi.org/10.1007/BF02274198

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