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DOI: 10.1039/A703654J (Paper) Reference Section for: Analyst, 1997, 122, 1521-1529

Multilevel Multifactor Designs for MultivariateCalibration

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Richard G. Brereton

Abstract

Multilevel experiments are common in chemistry, especially in calibration and mixture problems. This paper presents designs for l = 2–5 different concentration levels and l2 corresponding experiments. The importance of orthogonality between successive factors is discussed. It is shown that up to 12 mutually orthogonal factors can be generated for a five-level design. Methods of generating designs are generalised. The designs are restricted to first-order (linear) models, typical of most instrumental calibration experiments.

References

  1. H. Martens and T. Næs, Multivariate Calibration, Wiley, New York, 1989 Search PubMed .
  2. A. Höskuldsson, J. Chemom., 1988, 2, 211 .
  3. S. Wold, P. Geladi, K. Esbensen and J. Ohman, J. Chemom., 1987, 1, 41 CAS .
  4. R. G. Brereton, Analyst, 1995, 120, 2313 RSC .
  5. E. R. Malinowski, Factor Analysis in Chemistry, Wiley, New York, 2nd edn., 1991 Search PubMed .
  6. P. W. Araujo and R. G. Brereton, Analyst, 1995, 120, 2497 RSC .
  7. Analytical Methods Committee, Analyst, 1994, 119, 2363 Search PubMed .
  8. R. G. Krutchkoff, Technometrics, 1967, 9, 425 .
  9. R. G. Brereton, Chemometrics: Applications of Mathematics and Statistics to Laboratory Systems, Ellis Horwood, Chichester, 1993 Search PubMed .
  10. P. W. Araujo and R. G. Brereton, Trends Anal. Chem., 1996, 15, 63 CrossRef CAS .
  11. D. A. Cirovic, R. G. Brereton, P. T. Walsh, J. A. Ellwood and E. Scobbie, Analyst, 1995, 121, 575 Search PubMed .
  12. P. W. Araujo and R. G. Brereton, Analyst, 1997, 122, 621 RSC .
  13. M. A. Allus, R. G. Brereton and G. Nickless, Chemom. Intell. Lab. Syst., 1989, 6, 65 CrossRef CAS .
  14. E. Morgan, Chemometrics: Experimental Design, Wiley, Chichester, 1995 Search PubMed .
  15. S. N. Deming and S. L. Morgan, Experimental Design: A Chemometric Approach, Elsevier, Amsterdam, 2nd edn., 1993 Search PubMed .
  16. G. E. P. Box, W. G. Hunter and J. S. Hunter, Statistics for Experimenters, Wiley, New York, 1978 Search PubMed .
  17. R. L. Plackett and J. P. Burman, Biometrika, 1946, 33, 305 Search PubMed .
  18. W. L. Stevens, Ann. Eugenics, 1939, 9, 82 Search PubMed .
  19. L. Euler, Memoir presented to Academy of Science of St. Petersburg on 8th March 1779, published as Leonardi Euleri Opera Omnia, Sér. 1, 1932, 7, 291 Search PubMed .
  20. J. Dénes and G. L. Mullen, Discrete Math., 1993, 111, 157 CrossRef .
  21. N. Logothetis and H. P. Wynn, Quality Through Design: Experimental Design, Off-line Quality Control, and Taguchi's Contribution, Clarendon Press, Oxford, 1989 Search PubMed .
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