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Cited by 2,833Scientific Measurement and Uncertainty EvaluationAdvanced Measurement and Metrology TechniquesNumerical Methods and Algorithms

The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index; none of the 34 sources its claims cite is checked for support yet.

Guidelines for evaluating and expressing the uncertainty of NIST measurement results

Open access
Taylor, B N·1994·National Institute of Standards and Technology, NIST Technical Note 1297
DOI 10.6028/nist.tn.1297
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TL;DR

This NIST Technical Note 1297 (1994) gives guidelines for evaluating and expressing measurement uncertainty at NIST, adopting the CIPM/ISO Guide approach. It defines Type A and Type B evaluations, combined and expanded uncertainty, and reporting conventions, with \(k=2\) as the NIST default coverage factor.

Key findings

  • NIST policy: represent each uncertainty component by a standard uncertainty \(u_i\), combine them by the root-sum-of-squares method into the combined standard uncertainty \(u_c\), and report expanded uncertainty \(U = k u_c\) with \(k=2\) by convention, or report \(u_c\); other \(k\) values require established and documented requirements.
  • Type A evaluations use statistical methods; Type B evaluations use other means. The A/B distinction is not the same as “random”/“systematic.” Type B examples include dividing a quoted 95% interval by 1.960 and a 99% interval by 2.576; for a rectangular distribution \(u_j = a/\sqrt{3}\), for triangular \(u_j = a/\sqrt{6}\), and for normal models \(u_j \approx 1.48a\) for a 50% interval, \(u_j \approx a\) for 67%, and \(u_j \approx a/3\) for 99.73%.
  • Coverage: when the normal distribution applies and \(u_c\) has negligible uncertainty, \(U=2u_c\) defines an interval with approximately 95% confidence and \(U=3u_c\) greater than 99%. Table B.1 gives \(t\)-factors; for example, if \(\nu_{\text{eff}}=8\), \(k_{95}=2.3\) rather than 2.0.
  • Reporting examples use a nominal 100 g mass standard: \(m_s=(100.02147 \pm 0.00070)\) g with \(u_c=0.35\) mg and \(k=2\) gives approximately 95% confidence; a second example uses \(k=2.26\) based on \(t\) for \(\nu=9\); a third reports \(u_c=0.35\) mg with approximately 68% confidence. An end-gauge calibration uncertainty budget example gives combined standard uncertainty \(u_c(l)=34\) nm.

Methods

  • Design: consensus/guideline document, the 1994 second edition of NIST TN 1297, based on the CIPM 1981 recommendation and the ISO *Guide to the Expression of Uncertainty in Measurement*; intended for NIST measurement results.
  • Data or sample: no empirical sample; illustrative examples include a nominal 100 g mass standard and an end-gauge calibration uncertainty budget.
  • Main analysis: conceptual and policy guidance with formulas, including the law of propagation of uncertainty Eq. (A-3), Type A standard deviation of the mean Eq. (A-5), Type B assumed distributions, the Welch-Satterthwaite effective degrees of freedom, and \(t\)-distribution coverage factors.

Limitations

  • Stated in the paper: the guidance is not NIST policy unless directly quoted; the Technical Note does not give detailed statistical techniques for Type A evaluations; Type B degrees of freedom are “more problematic”; the coverage-factor procedure is approximate and “should not be interpreted as being rigourous”; and it is generally not possible to know all uses of a measurement result.
  • Stated in the paper: Type B evaluations depend on scientific judgment and available information, and Type A evaluations based on limited data are not necessarily more reliable than soundly based Type B evaluations.
  • Evident from the text: this is a policy/guidance document rather than an empirical validation study, and its numerical examples are illustrative rather than generalizable results.

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Integrity signals

Registry

Crossref · 10.6028/nist.tn.1297

Cites

8 of 8 references verified0 citation errors · 0 not checkable

Statistics

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Verification

Claims the paper makes

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Show all 30 claims

  • Probably not a substantial claim. 49
  • The quote only partly states this claim. 1
  • It may state two separate claims as one. 10
53 of 53

  • The paper relies on this without support.

    In October 1992, a new policy on expressing measurement uncertainty was instituted at NIST.

    “In October 1992, a new policy on expressing measurement uncertainty was instituted at NIST.”

  • The paper relies on this without support.

    In general, the result of a measurement is only an approximation or estimate of the value of the measurand, and thus the result is complete only when accompanied by a quantitative statement of its uncertainty.

    “In general, the result of a measurement is only an approximation or estimate of the value of the specific quantity subject to measurement, that is, the measurand, and thus the result is complete only when accompanied by a quantitative statement of its uncertainty.”

  • The paper relies on this without support.

    Although the vast majority of NIST measurement results are accompanied by quantitative statements of uncertainty, there has never been a uniform approach at NIST to the expression of uncertainty.

    “Although the vast majority of NIST measurement results are accompanied by quantitative statements of uncertainty, there has never been a uniform approach at NIST to the expression of uncertainty.”

  • The paper relies on this without support.

    It is generally agreed that the usefulness of measurement results, and thus much of the information that NIST provides as an institution, is to a large extent determined by the quality of the statements of uncertainty that accompany them.

    “It is generally agreed that the usefulness of measurement results, and thus much of the information that we provide as an institution, is to a large extent determined by the quality of the statements of uncertainty that accompany them.”

  • The paper relies on this without support.

    The Guide represents the current international view of how to express uncertainty in measurement based on the CIPM approach.

    “Although the Guide represents the current international view of how to express uncertainty in measurement based on the CIPM approach, it is a rather lengthy document.”

  • The authors state this as an assumption.

    A correction (or correction factor) is applied to compensate for each recognized systematic effect that significantly influences the measurement result, and every effort has been made to identify such effects.

    “It is assumed that a correction (or correction factor) is applied to compensate for each recognized systematic effect that significantly influences the measurement result and that every effort has been made to identify such effects.”

  • The paper relies on this without support.

    The reliability of evaluations of components of uncertainty depends on the quality of the information available.

    “Because the reliability of evaluations of components of uncertainty depends on the quality of the information available, it is recommended that all parameters upon which the measurand depends be varied to the fullest extent practicable so that the evaluations are based as much as possible on observed data.”

  • The paper relies on this without support.

    For some commercial, industrial, and regulatory applications of NIST results, a measure of uncertainty that defines an interval about the measurement result within which the value of the measurand is confidently believed to lie is often required.

    “for some commercial, industrial, and regulatory applications of NIST results (e.g., when health and safety are concerned), what is often required is a measure of uncertainty that defines an interval about the measurement result y within which the value of the measurand Y is confidently believed to lie.”

  • The authors state this as an assumption.

    The possible estimated values of the standard are approximately normally distributed with approximate standard deviation u_c.

    “Since it can be assumed that the possible estimated values of the standard are approximately normally distributed with approximate standard deviation u , the c”

  • The paper relies on this without support.

    Some users of NIST measurement results may automatically interpret U = 2u_c and u_c as defining intervals with levels of confidence of 95 percent and 68 percent, respectively.

    “Some users of NIST measurement results may automatically interpret U = 2u and u as quantities that c c define intervals having levels of confidence corresponding to those of a normal distribution, namely, 95 percent and 68 percent, respectively.”

  • The paper relies on this without support.

    It is not possible to know in detail all uses to which a particular NIST measurement result will be put.

    “In general, it is not possible to know in detail all of the uses to which a particular NIST measurement result will be put.”

  • The paper relies on this without support.

    It is common practice to carry out Type B evaluations in a manner that ensures underestimation is avoided.

    “However, it is common practice to carry out such evaluations in a manner that ensures that an underestimation is avoided.”

  • The paper relies on this without support.

    When lower and upper limits are set for Type B evaluations, they are usually chosen so that the probability of the quantity lying outside these limits is extremely small.

    “For example, when lower and upper limits a and a + are set as in the case discussed in subsection A.5, they are usually chosen in such a way that the probability of the quantity in question lying outside these limits is in fact extremely small.”

  • The paper relies on this without support.

    Precision is often taken to mean simply repeatability.

    “Nevertheless, precision is often taken to mean simply repeatability.”

  • The paper relies on this without support.

    It will take some time before the meanings of standard uncertainty, combined standard uncertainty, expanded uncertainty, and their relative forms become well known.

    “However, since it will take some time before the meanings of these terms become well known, they should be defined at the beginning of a paper or when first used.”
15 of 15

Citations

Cites

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Show all 7 references

Research works printed but not linked: 5

  1. CIPM, BIPM Proc.-Verb. Com. Int. Poids et Mesures 54, 14, 35 (1986) (in French);
  2. CIPM, BIPM Proc. Verb. Com. Int. Poids et Mesures Measurement Results, NIST Technical Note 1297, 49, 8-9, 26 (1981) (in French);
  3. CIPM, BIPM Proc.-Verb. Com. Int. Poids et Mesures 54, 14, 35 (1986) (in French);
  4. 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);
  5. I, H. H. Ku, Editor (U.S. Government Printing Office, Washington, DC, 1969), pp. 21-48.

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Metadata

Authors
Taylor, B. N.
Affiliations
National Institute of Standards and Technology (US)
Corresponding author
Taylor, B N
ORCID
Taylor, B N
Venue
National Institute of Standards and Technology, NIST Technical Note 1297
Publisher
National Bureau of Standards
Published
1994
DOI
10.6028/nist.tn.1297
OpenAlex
W4300497458
Cited by
2,833
References
7
Citations by year
2026: 82 · 2025: 104 · 2024: 109 · 2023: 110 · 2022: 133 · 2021: 141 · 2020: 156 · 2019: 141 · 2018: 150 · 2017: 135 · 2016: 116 · 2015: 105 · 2014: 103 · 2013: 100 · 2012: 112
Type
report
Language
en
Open access
Topics
  • Physical Sciences › Physics and Astronomy › Instrumentation › Scientific Measurement and Uncertainty Evaluation
  • Physical Sciences › Engineering › Mechanical Engineering › Advanced Measurement and Metrology Techniques
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Numerical Methods and Algorithms
Keywords
measurement uncertainty, uncertainty analysis, uncertainty expression, measurement results, NIST guidelines

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