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Analytical Methods for the Propagation of Uncertainties

In: Introduction to Statistics in Metrology

Author

Listed:
  • Stephen Crowder

    (Sandia National Laboratories)

  • Collin Delker

    (Sandia National Laboratories)

  • Eric Forrest

    (Sandia National Laboratories)

  • Nevin Martin

    (Sandia National Laboratories)

Abstract

An indirect measurement is a measurement where multiple quantities are measured and combined through a model equation to obtain the value of the measurand. This chapter presents analytical methods for determining the uncertainty in the measurand when the individual measured quantities each have their own uncertainty. A full derivation of what is commonly known as the GUM method is provided, for the cases of both uncorrelated and correlated input measurements. Nonlinear models and higher-order terms are also discussed, along with the case where the measurement model results in multiple output quantities. Finally, some limitations and assumptions of this analytical approach are presented.

Suggested Citation

  • Stephen Crowder & Collin Delker & Eric Forrest & Nevin Martin, 2020. "Analytical Methods for the Propagation of Uncertainties," Springer Books, in: Introduction to Statistics in Metrology, chapter 0, pages 131-151, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-53329-8_7
    DOI: 10.1007/978-3-030-53329-8_7
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