Accreditation and Quality Assurance

, Volume 13, Issue 6, pp 293–298 | Cite as

Application of consistency checking to evaluation of uncertainty in multiple replicate measurements

General Paper


Use of repeated measurements in quantitative chemical analysis is common but leads to the problem of how to combine the measurement values and produce a result with an uncertainty following the GUM. There is often confusion between repeated indications or observations of an input quantity, for whose uncertainty the GUM prescribes a type A evaluation, and complete measurements repeated on multiple sub-samples, as considered here. A solution for combining repeated measurement results and their individual uncertainties based on simple interval logic is proposed here. The individual measurement values and their uncertainties are compared with the calculated average value to see if this implies that another, possibly unknown, source of uncertainty is present. The model of the individual results is modified for this possible between-replicate effect so that the repeated measurements are consistent. Lack of consistency is a strong indication that the measurement is not fully under control and needs further development or investigation. This is not always possible, however and the method given here is proposed to ensure that the values of the repeated measurements agree with each other. A simple numerical example is given showing how the method can be implemented in practice.


Uncertainty of measurement Multiple replicates Consistency test Repeated measurements 


  1. 1.
    Ellison SLR, Rösslein M, Williams A, Eurachem/Citac (eds) (2000) Quantifying uncertainty in analytical measurement, 2nd edn.
  2. 2.
    European co-operation for Accreditation (1999) Expression of the uncertainty of measurement in calibration, EA, EA-4/02.
  3. 3.
    International Organization for Standardization (1995) Guide to the Expression of Uncertainty in Measurement, 2nd edn. International Organization for Standardization, Geneva, ISBN 92-67-10188-9Google Scholar
  4. 4.
    Kessel R (2003) A novel approach to uncertainty evaluation of complex measurements in isotope chemistry, Dissertation. University of Antwerp, AntwerpGoogle Scholar
  5. 5.
    Box GEP, Hunter WG, Hunter JS (1978) Statistics for experimenters. Wiley, NY, ISBN 0-471-09315-7Google Scholar
  6. 6.
    ISO: GUIDE 35 (1989) Certification of reference materials, 2nd edn. International Organisation for Standardisation, GenevaGoogle Scholar
  7. 7.
    GUM Workbench Version 2.3.6 2005 Metrodata GmbH, Im Winkel 15-1, D-79576, Weil am Rhein, Germany.
  8. 8.
    Kessel R, Berglund M, Taylor P, Wellum R (2000) How to treat correlation in the uncertainty budget, when combining results from different measurements, paper presented at AMCTM 2000, ISBN 981-02-4494-0Google Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Rüdiger Kessel
    • 1
  • Michael Berglund
    • 2
  • Roger Wellum
    • 2
  1. 1.Metrodata GmbHWeil am RheinGermany
  2. 2.Institute for Reference Materials and MeasurementsGeelBelgium

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