of the NIST Administrative Manual

ASSOCIATED WITH MEASUREMENT RESULTS

Equally important, the CIPM approach has come into use in a significant number of areas at NIST and is also becoming accepted in U.S. industry. For example, the National Conference of Standards Laboratories (NCSL) is using it to develop a Recommended Practice on measurement uncertainty for NCSL member laboratories.

The CIPM approach is based on Recommendation INC-1 (1980) of the Working Group
on the Statement of Uncertainties [3]. This group was
convened in 1980 by the International Bureau of Weights and Measures (BIPM)
in response to a request by the CIPM. More recently, at the request of the CIPM,
a joint BIPM/IEC/ISO/OIML working group developed a comprehensive reference
document on the general application of the CIPM approach titled *Guide to the
Expression of Uncertainty in Measurement* [4] (IEC:
International Electrotechnical Commission; ISO: International Organization for
Standardization; OIML: International Organization of Legal Metrology). The
development of the *Guide* is providing further impetus to the worldwide
adoption of the CIPM approach.

- 1)
*Standard Uncertainty*: Represent each component of uncertainty that contributes to the uncertainty of the measurement result by an estimated standard deviation*u*, termed_{i }**standard uncertainty**, equal to the positive square root of the estimated variance*u*_{i}^{2}. - 2)
*Combined Standard Uncertainty*: Determine the**combined standard uncertainty***u*_{c}of the measurement result, taken to represent the estimated standard deviation of the result, by combining the individual standard uncertainties*u*(and covariances as appropriate) using the usual "root-sum-of-squares" method, or equivalent established and documented methods._{i}Commonly,

*u*_{c}is used for reporting results of determinations of fundamental constants, fundamental metrological research, and international comparisons of realizations of SI units. - 3)
*Expanded Uncertainty*: Determine an**expanded uncertainty***U*by multiplying*u*_{c}by a**coverage factor***k*:*U*=*k**u*_{c}. The purpose of*U*is to provide an interval*y*-*U*to*y*+*U*about the result*y*within which the value of*Y*, the specific quantity subject to measurement and estimated by*y*, can be asserted to lie with a high level of confidence. Thus one can confidently assert that*y*-*U*≤*Y*≤*y*+*U*, which is commonly written as*Y*=*y*±*U*.Use expanded uncertainty

*U*to report the results of all NIST measurements other than those for which*u*_{c}has traditionally been employed. To be consistent with current international practice, the value of*k*to be used at NIST for calculating*U*is, by convention,*k*= 2. Values of*k*other than 2 are only to be used for specific applications dictated by established and documented requirements. - 4)
*Reporting Uncertainty*: Report*U*together with the coverage factor*k*used to obtain it, or report*u*_{c}.When reporting a measurement result and its uncertainty, include the following information in the report itself or by referring to a published document:

- - A list of all components of standard uncertainty, together with their
degrees of freedom where appropriate, and the resulting value of
*u*_{c}. The components should be identified according to the method used to estimate their numerical values: - A. those which are evaluated by statistical methods,
- B. those which are evaluated by other means.
- - A detailed description of how each component of standard uncertainty
was evaluated.
- - A description of how
*k*was chosen when*k*is not taken equal to 2.

- - A list of all components of standard uncertainty, together with their
degrees of freedom where appropriate, and the resulting value of

Additional guidance on the use of the CIPM approach at NIST may be found in
*Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement
Results* [5]. A more detailed discussion of the CIPM
approach is given in the *Guide to the Expression of Uncertainty in
Measurement* [4]. Classic expositions of the statistical
evaluation of measurement processes are given in references
[6-8].

b. The Statistical Engineering Division, Computing and Applied Mathematics Laboratory, is responsible for providing technical advice on statistical methods for evaluating and expressing the uncertainty of NIST measurement results.

c. NIST Editorial Review Boards are responsible for ensuring that statements of measurement uncertainty are included in NIST publications and other technical outputs under their jurisdiction which report measurement results and that such statements are in conformity with this policy.

d. The Calibrations Advisory Group is responsible for ensuring that calibration and test reports and other technical outputs under its jurisdiction are in compliance with this policy.

e. The Standard Reference Materials and Standard Reference Data programs are responsible for ensuring that technical outputs under their jurisdiction are in compliance with this policy.

f. Authors, as part of the process of preparing manuscripts and other technical outputs, are responsible for formulating measurement uncertainty statements consistent with this policy. These statements must be present in drafts submitted for NIST review and approval.

[2] CIPM, *BIPM Proc.-Verb. Com. Int.
Poids et Mesures* **54**, 14, 35 (1986) (in French); P. Giacomo,
"News from the BIPM," Metrologia **24**, 45-51 (1987).

[3] R. Kaarls, "Rapport du Groupe de
Travail sur l'Expression des Incertitudes au Comité International des
Poids et Mesures," *Proc.-Verb. Com. Int. Poids et Mesures*
**49**, A1-A12 (1981) (in French); P. Giacomo, "News from the
BIPM," *Metrologia* **17**, 69-74 (1981). (Note that the final
English-language version of Recommendation INC-1 (1980), published in an
internal BIPM report, differs slightly from that given in the latter reference
but is consistent with the authoritative French-language version given in the
former reference.)

[4] ISO, *Guide to the Expression of Uncertainty in
Measurement*, prepared by ISO Technical Advisory Group 4 (TAG 4),
Working Group 3 (WG 3), October 1993. ISO/TAG 4 has as its
sponsors the BIPM, IEC, IFCC (International Federation of Clinical Chemistry),
ISO, IUPAC (International Union of Pure and Applied Chemistry), IUPAP
(International Union of Pure and Applied Physics), and OIML. Although the
individual members of WG 3 were nominated by the BIPM, IEC, ISO, or OIML,
the *Guide* is published by ISO in the name of all seven organizations.
NIST staff members may obtain a single copy of the *Guide* from the NIST
Calibration Program.

[5] B.N. Taylor and C.E. Kuyatt, *Guidelines for
Evaluating and Expressing the Uncertainty of NIST Measurement Results*,
NIST Technical Note 1297, prepared under the auspices of the NIST
*Ad Hoc* Committee on Uncertainty Statements (U.S. Government Printing
Office, Washington, DC, 1993).

[6] C. Eisenhart, "Realistic Evaluation of the Precision
and Accuracy of Instrument Calibration Systems," *J. Res. Natl. Bur.
Stand.* (U.S.) **67C**, 161-187 (1963). Reprinted, with corrections,
in *Precision Measurement and Calibration: Statistical Concepts and
Procedures*, NBS Special Publication 300, Vol. I, H.H. Ku, Editor
(U.S. Government Printing Office, Washington, DC, 1969), pp. 21-48.

[7] J. Mandel, *The Statistical Analysis of Experimental
Data*, (Interscience-Wiley Publishers, New York, NY, 1964, out of print;
corrected and reprinted, Dover Publishers, New York, NY, 1984).

[8] M.G. Natrella, *Experimental Statistics*, NBS
Handbook 91 (U.S. Government Printing Office, Washington, DC, 1963;
reprinted October 1966 with corrections).