The NIST Reference on Constants, Units and Uncertainty

Uncertainty of Measurement Results
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A measurement result is complete only when accompanied by a quantitative statement of its uncertainty. The uncertainty is required in order to decide if the result is adequate for its intended purpose and to ascertain if it is consistent with other similar results.

International and U.S. perspectives on measurement uncertainty

Over the years, many different approaches to evaluating and expressing the uncertainty of measurement results have been used. Because of this lack of international agreement on the expression of uncertainty in measurement, in 1977 the International Committee for Weights and Measures (CIPM, Comité International des Poids et Measures), the world's highest authority in the field of measurement science (i.e., metrology), asked the International Bureau of Weights and Measures (BIPM, Bureau International des Poids et Mesures), to address the problem in collaboration with the various national metrology institutes and to propose a specific recommendation for its solution. This led to the development of Recommendation INC-1 (1980) by the Working Group on the Statement of Uncertainties convened by the BIPM, a recommendation that the CIPM approved in 1981 and reaffirmed in 1986 via its own Recommendations 1 (CI-1981) and 1 (CI-1986):

    Recommendation INC-1 (1980)
    Expression of experimental uncertainties

    1. The uncertainty in the result of a measurement generally consists of several components which may be grouped into two categories according to the way in which their numerical value is estimated.

      Type A. Those which are evaluated by statistical methods

      Type B. Those which are evaluated by other means

    There is not always a simple correspondence between the classification into categories A or B and the previously used classification into "random" and "systematic" uncertainties. The term "systematic uncertainty" can be misleading and should be avoided.

    Any detailed report of uncertainty should consist of a complete list of the components, specifying for each the method used to obtain its numerical value.


2. The components in category A are characterized by the estimated variances si2 ( or the estimated "standard deviations" si) and the number of degrees of freedom vi. Where appropriate the covariances should be given.

3. The components in category B should be characterized by quantities uj2, which may be considered approximations to the corresponding variances, the existence of which is assumed. The quantities uj2 may be treated like variances and the quantities uj like standard deviations. Where appropriate, the covariances should be treated in a similar way.

4. The combined uncertainty should be characterized by the numerical value obtained by applying the usual method for the combination of variances. The combined uncertainty and its components should be expressed in the form of "standard deviations."

5. If for particular applications, it is necessary to multiply the combined uncertainty by an overall uncertainty, the multiplying factor must always be stated.

The above recommendation, INC-1 (1980), is a brief outline rather than a detailed prescription. Consequently, the CIPM asked the International Organization for Standardization (ISO) to develop a detailed guide based on the recommendation because ISO could more easily reflect the requirements stemming from the broad interests of industry and commerce. The ISO Technical Advisory Group on Metrology (TAG 4) was given this responsibility. It in turn established Working group 3 and assigned it the following terms of reference:

    To develop a guidance document based upon the recommendation of the BIPM Working Group on the Statement of Uncertainties which provides rules on the expression of measurement uncertainty for use within standardization, calibration, laboratory accreditation, and metrology services;

    The purpose of such guidance is:

      to promote full information on how uncertainty statements are arrived at;
      to provide a basis for the international comparison of measurement results.

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